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HW7 Due: 11:59pm on Sunday, November 18, 2018

You will receive no credit for items you complete after the assignment is due. Grading Policy

Exercise 28.10

A short current element = (0.500 ) carries a current of 4.60 in the same direction as . Point is located at = ( -0.730 ) + (0.390 ) .

Part A

Find the magnetic field at produced by this current element.

Enter the , , and components of the magnetic field separated by commas.

ANSWER:

Exercise 28.24

A rectangular loop with dimensions 4.20 by 9.50 carries current . The current in the loop produces a magnetic field at the center of the loop that has magnitude 5.20×10−5 and direction away from you as you view the plane of the loop.

Part A

What is the magnitude of the current in the loop?

Express your answer with the appropriate units.

ANSWER:

Part B

What is the direction of the current in the loop?

ANSWER:

Exercise 28.36

A closely wound, circular coil with radius 2.20 has 760 turns.

dl ⃗  mm ĵ A dl ⃗  P

r ⃗  m î m k̂

P

x y z

, , = dBx dBy dBz T

cm cm I T

= I

clockwise

counterclockwise

cm

11/30/2018 HW7

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Part A

What must the current in the coil be if the magnetic field at the center of the coil is 0.0760 ?

Express your answer to three significant figures and include the appropriate units.

ANSWER:

Part B

At what distance from the center of the coil, on the axis of the coil, is the magnetic field half its value at the center?

Express your answer to three significant figures and include the appropriate units.

ANSWER:

Exercise 28.39

Two round concentric metal wires lie on a tabletop, one inside the other. The inner wire has a diameter of 23.0 and carries a clockwise current of 16.0 , as viewed from above, and the outer wire has a diameter of 40.0 .

Part A

What must be the direction (as viewed from above) of the current in the outer wire so that the net magnetic field due to this combination of wires is zero at the common center of the wires?

ANSWER:

Part B

What must be the magnitude of the current in the outer wire so that the net magnetic field due to this combination of wires is zero at the common center of the wires?

ANSWER:

Exercise 28.34

Part A

T

= I

x

= x

cm A cm

The current's direction must be clockwise.

The current's direction must be counterclockwise.

= I A

11/30/2018 HW7

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Calculate the magnitude of the magnetic field at point P due to the current in the semicircular section of wire shown in the figure . (Hint: Does the current in the long, straight section of the wire produce any field at P?)

Express your answer in terms of the variables , and appropriate constants.

ANSWER:

Part B

Find the direction of the magnetic field at point P.

ANSWER:

Exercise 28.26

Four very long, current-carrying wires in the same plane intersect to form a square with sidelengths 32.0 , as shown in the figure .

I R

into the page

out of the page

cm

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Part A

Find the magnitude of the current so that the magnetic field at the center of the square is zero.

Express your answer using two significant figures.

ANSWER:

Part B

Find the direction of the current so that the magnetic field at the center of the square is zero.

ANSWER:

Exercise 28.44

A solid conductor with radius a is supported by insulating disks on the axis of a conducting tube with inner radius and outer radius (). The central conductor and tube carry currents and correspondingly in the same direction. The currents are distributed uniformly over the cross sections of each conductor. Derive an expression for the magnitude of the magnetic field

Part A

at points outside the central, solid conductor but inside the tube

Express your answer in terms of the variables , , ( ), and appropriate constants ( and ).

ANSWER:

I

= I A

I

upward

downward

b c I1 I2

I1 I2 r a < r < b μ0 π

= B(r)

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Part B

at points outside the tube

Express your answer in terms of the variables , , ( ), and appropriate constants ( and ).

ANSWER:

Exercise 28.51

A wooden ring whose mean diameter is 14.0 is wound with a closely spaced toroidal winding of 595 turns.

Part A

Compute the magnitude of the magnetic field at the center of the cross section of the windings when the current in the windings is 0.670 .

ANSWER:

Exercise 28.54

The current in the windings of a toroidal solenoid is 2.700 . There are 490 turns and the mean radius is 23.00 . The toroidal solenoid is filled with a magnetic material. The magnetic field inside the windings is found to be 1.920 .

Part A

Calculate the relative permeability.

Express your answer using four significant figures.

ANSWER:

Part B

Calculate the magnetic susceptibility of the material that fills the toroid.

Express your answer using four significant figures.

ANSWER:

Conceptual Question 28.01

I1 I2 r r > c μ0 π

= B(r)

cm

A

= B T

A cm T

= Km

= χm

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Part A

A vertical wire carries a current straight down. To the east of this wire, the magnetic field points

ANSWER:

Conceptual Question 28.04

Part A

Two long parallel wires placed side-by-side on a horizontal table carry identical size currents in opposite directions. The wire on your right carries current toward you, and the wire on your left carries current away from you. From your point of view, the magnetic field at the point exactly midway between the two wires

ANSWER:

Conceptual Question 28.09

Part A

Two very long parallel wires in the xy-plane, a distance 2 apart, are parallel to the y-axis and carry equal currents as shown in the figure. The + direction points perpendicular to the xy-plane in a right-handed coordinate system. If both currents flow in the + direction, which one of the graphs shown in the figure below best represents the component of the net magnetic field, in the xy-plane, as a function of ? (Caution: These graphs are not magnetic field lines.)

toward the south.

toward the north.

toward the west.

downward.

toward the east.

points downward.

points upward.

is zero.

points toward you.

points away from you.

a I z

y z x

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ANSWER:

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Conceptual Question 28.10

Part A

Two very long parallel wires in the xy-plane, a distance 2 apart, are parallel to the y-axis and carry equal currents as shown in the figure. The + direction points perpendicular to the xy-plane in a right-handed coordinate system. If the left current flows in the + direction and the right current flows in the -y direction, which one of the graphs shown in the figure below best represents the component of the net magnetic field, in the xy-plane, as a function of ? (Caution: These graphs are not magnetic field lines.)

1

2

3

4

5

a I z

y z x

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ANSWER:

Conceptual Question 28.11

Part A

1

2

3

4

5

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The figure shows three long, parallel current-carrying wires. The magnitudes of the currents are equal and their directions are indicated in the figure. Which of the arrows drawn near the wire carrying current 1 correctly indicates the direction of the magnetic force acting on that wire?

ANSWER:

Conceptual Question 28.13

Part A

A long straight conductor has a constant current flowing to the right. A wire rectangle is situated above the wire, and also has a constant current flowing through it (as shown in the figure). Which of the following statements is true?

ANSWER:

A

B

C

D

The magnetic force on current 1 is equal to zero.

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Conceptual Question 28.15

Part A

A very long, hollow, thin-walled conducting cylindrical shell (like a pipe) of radius carries a current along its length uniformly distributed throughout the thin shell. Which one of the graphs shown in the figure most accurately describes the magnitude of the magnetic field produced by this current as a function of the distance from the central axis?

ANSWER:

The net magnetic force on the wire rectangle is zero, and the net torque on it is zero.

The net magnetic force on the wire rectangle is downward, and the net torque on it is zero.

The net magnetic force on the wire rectangle is downward, and there is also a net torque on the it.

The net magnetic force on the wire rectangle is zero, but there is a net torque on it.

The net magnetic force on the wire rectangle is upward, and there is also a net torque on the it.

R

B r

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Conceptual Question 28.17

Part A

Consider a solenoid of length , windings, and radius ( is much longer than ). A current is flowing through the wire. If the radius of the solenoid were doubled (becoming 2b), and all other quantities remained the same, the magnetic field inside the solenoid would

ANSWER:

Prelecture Concept Question 28.04

Part A

Two long parallel wires are placed side by side on a horizontal table. The wires carry equal currents in the same direction. Which of the following statements are true?

Check all that apply.

ANSWER:

Prelecture Concept Question 28.01

1

2

3

4

5

L N b L b I

become one half as strong.

become twice as strong.

remain the same.

The magnetic force between the two wires is attractive.

The magnetic field at a point midway between the two wires is zero.

The magnetic field is a maximum at a point midway between the two wires.

The magnetic force between the two wires is repulsive.

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Part A

Which of the following statements are true concerning the creation of magnetic fields?

Check all that apply.

ANSWER:

Problem 28.04

Part A

A very long thin wire produces a magnetic field of 5×10−3 × 10-4 T at a distance of 1 mm. from the central axis of the wire. What is the magnitude of the current in the wire? (μ 0 = 4π × 10-7 T · m/A)

ANSWER:

Problem 28.02

Part A

A point charge Q moves on the x-axis in the positive direction with a speed of 370 m/s. A point P is on the y-axis at y = +50 mm. The magnetic field produced at point P, as the charge moves through the origin, is equal to -0.7 μT . When the charge is at x = +40 mm, what is the magnitude of the magnetic field at point P? (μ 0 = 4π × 10-7 T · m/A)

ANSWER:

A distribution of electric charges at rest creates a magnetic field at all points in the surrounding region.

A single stationary electric charge creates a magnetic field at all points in the surrounding region.

An electric current in a conductor creates a magnetic field at all points in the surrounding region.

A moving electric charge creates a magnetic field at all points in the surrounding region.

A permanent magnet creates a magnetic field at all points in the surrounding region.

5.0 mA

1.0×104 mA

2.5 mA

7900 mA

k̂

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Problem 28.18

Part A

A long straight wire on the -axis carries a current of 6.0 A in the positive direction. A circular loop in the xy-plane, of radius 10 cm, carries a 1.0-A current, as shown in the figure. Point , at the center of the loop, is 25 cm from the -axis. An electron is projected from with a velocity of 1.0 × 106 m/s in the negative -direction. What is the component of the force on the electron? ( = 1.60 × 10-19 C, μ 0 = 4π × 10-7 T · m/A)

ANSWER:

Problem 28.21

0.33 μT

0.63 μT

0.53 μT

0.43 μT

0.73 μT

z P z

P x y

e

-2.0 × 10-18 N

+1.0 × 10-18 N

-1.0 × 10-18 N

+2.0 × 10-18 N

zero

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Part A

As shown in the figure, a wire is bent into the shape of a tightly closed omega ( ), with a circular loop of radius 4.0 cm and two long straight sections. The loop is in the xy-plane, with the center at the origin. The straight sections are parallel to the

-axis. The wire carries a 5.0-A current, as shown. What is the magnitude of the magnetic field at the center of the loop? (μ 0 = 4π × 10-7 T · m/A)

ANSWER:

Problem 28.30

Part A

A cylindrical insulated wire of diameter 4.0 mm is tightly wound 300 times around a cylindrical core to form a solenoid with adjacent coils touching each other. When a 0.30 A current is sent through the wire, what is the magnitude of the magnetic field on the axis of the solenoid near its center? (μ 0 = 4π × 10-7 T · m/A)

ANSWER:

Problem 28.68

Ω

x

80 µT

25 µT

40 µT

54 µT

104 µT

11.2 × 10-5 T

4.7 × 10-5 T

5.2 × 10-5 T

9.4 × 10-5 T

7.8 × 10-5 T

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In the wire shown in segment is an arc of a circle with radius 30.0 , and point is at the center of curvature of the arc. Segment

is an arc of a circle with radius 20.0 , and point is at its center of curvature. Segments and are straight lines of length 10.0 each.

Part A

Calculate the magnitude of the magnetic field at a point due to a current 11.0 in the wire.

Express your answer with the appropriate units

ANSWER:

Part B

What is the direction of magnetic field?

ANSWER:

Score Summary: Your score on this assignment is 0.0%.

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BC cm P

DA cm P CD AB

cm

P A

= B

into the page

out of the page

11/30/2018 HW2

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HW2 Due: 11:59pm on Monday, September 24, 2018

You will receive no credit for items you complete after the assignment is due. Grading Policy

Exercise 22.2

A flat sheet is in the shape of a rectangle with sides of lengths 0.400 and 0.600 . The sheet is immersed in a uniform electric field of magnitude 60.0 that is directed at 20 from the plane of the sheet .

Part A

Find the magnitude of the electric flux through the sheet.

Express your answer to two significant figures and include the appropriate units.

ANSWER:

Exercise 22.4

It was shown in Example 21.11 (Section 21.5) in the textbook that the electric field due to an infinite line of charge is perpendicular to the line and has magnitude . Consider an imaginary cylinder with a radius of = 0.130 and a length of = 0.430 that has an infinite line of positive charge running along its axis. The charge per unit length on the line is = 7.20 .

Part A

What is the electric flux through the cylinder due to this infinite line of charge?

ANSWER:

Part B

m m N/C ∘

= Φ

E = λ/2π rϵ0 r m l m λ

μC/m

= Φ /CN ⋅ m2

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What is the flux through the cylinder if its radius is increased to 0.505 ?

ANSWER:

Part C

What is the flux through the cylinder if its length is increased to 0.810 ?

ANSWER:

Exercise 22.9

A charged paint is spread in a very thin uniform layer over the surface of a plastic sphere of diameter 18.0 , giving it a charge of -49.0 .

Part A

Find the electric field just inside the paint layer.

Express your answer with the appropriate units. Enter positive value if the field is directed away from the center of the sphere and negative value if the field is directed toward the center of the sphere.

ANSWER:

Part B

Find the electric field just outside the paint layer.

Express your answer with the appropriate units. Enter positive value if the field is directed away from the center of the sphere and negative value if the field is directed toward the center of the sphere.

ANSWER:

Part C

Find the electric field 5.00 outside the surface of the paint layer.

Express your answer with the appropriate units. Enter positive value if the field is directed away from the center of the sphere and negative value if the field is directed toward the center of the sphere.

ANSWER:

r = m

= Φ /CN ⋅ m2

l = m

= Φ /CN ⋅ m2

cm μC

= E

= E

cm

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Gauss's Law

Learning Goal:

To understand the meaning of the variables in Gauss's law, and the conditions under which the law is applicable.

Gauss's law is usually written

where is the permittivity of vacuum.

Part A

How should the integral in Gauss's law be evaluated?

ANSWER:

Part B Complete previous part(s)

Exercise 22.12

The nuclei of large atoms, such as uranium, with protons, can be modeled as spherically symmetric spheres of charge. The radius of the uranium nucleus is approximately .

Part A

What is the electric field this nucleus produces just outside its surface?

Express your answer using two significant figures.

ANSWER:

Part B

What magnitude of electric field does it produce at the distance of the electrons, which is about 1.9×10−10 ?

Express your answer using two significant figures.

= E

= ∮ ⋅d = ,ΦE E⃗  A⃗  qencl ϵ0

= 8.85 × /(N ⋅ )ϵ0 10 −12 C2 m2

around the perimeter of a closed loop

over the surface bounded by a closed loop

over a closed surface

92 7.4 × m10−15

= E N/C

m

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ANSWER:

Part C

The electrons can be modeled as forming a uniform shell of negative charge. What net electric field do they produce at the location of the nucleus?

Express your answer using two significant figures.

ANSWER:

A Charged Sphere with a Cavity

An insulating sphere of radius , centered at the origin, has a uniform volume charge density .

Part A

Find the electric field inside the sphere (for < ) in terms of the position vector .

Express your answer in terms of , (Greek letter rho), and .

You did not open hints for this part.

ANSWER:

Part B Complete previous part(s)

± The Charge on a Thundercloud

In a thunderstorm, charge builds up on the water droplets or ice crystals in a cloud. Thus, the charge can be considered to be distributed uniformly throughout the cloud. For the purposes of this problem, take the cloud to be a sphere of diameter 1.00 kilometer. The point of this problem is to estimate the maximum amount of charge that this cloud can contain, assuming that the charge builds up until the electric field at the surface of the cloud reaches the value at which the surrounding air breaks down. This breakdown means that the air becomes highly ionized, enabling it to conduct the charge from the cloud to the ground or another nearby cloud. The ionized air will then emit light due to the recombination of the electrons and atoms to form excited molecules that radiate light. In addition, the large current will heat up the air, resulting in its rapid expansion. These two phenomena account for the appearance of lightning and the sound of thunder. Take the breakdown electric field of air to be

.

Part A

Estimate the total charge on the cloud when the breakdown of the surrounding air is reached.

= E N/C

= Enet N/C

a ρ

( )E ⃗  r ⃗  r a r ⃗ 

r ⃗  ρ ϵ0

= ( )E ⃗  r ⃗ 

= 3.00 × N/CEb 10 6

q

11/30/2018 HW2

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Express your answer numerically, to three significant figures, using .

You did not open hints for this part.

ANSWER:

Charge Distribution on a Conducting Shell - 2

A positive charge is kept (fixed) off-center inside a fixed spherical conducting shell that is electrically neutral, and the charges in the shell are allowed to reach electrostatic equilibrium.

Part A

The large positive charge inside the shell is roughly 16 times that of the smaller charges shown on the inner and outer surfaces of the spherical shell. Which of the following figures best represents the charge distribution on the inner and outer walls of the shell?

You did not open hints for this part.

ANSWER:

Charge Distribution on a Conducting Shell - 1

A positive charge is kept (fixed) at the center inside a fixed spherical neutral conducting shell.

= 8.85 × /(N ⋅ )ϵ0 10 −12 C2 m2

= Coulombs q

1

2

3

4

5

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Part A

The positive charge is equal to roughly 16 of the smaller charges shown on the surfaces of the spherical shell. Which of the pictures best represents the charge distribution on the inner and outer walls of the shell?

You did not open hints for this part.

ANSWER:

Conceptual Question 22.01

Part A

If the electric flux through a closed surface is zero, the electric field at points on that surface must be zero.

ANSWER:

Conceptual Question 22.02

1

2

3

4

5

True

False

11/30/2018 HW2

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Part A

The figure shows four Gaussian surfaces surrounding a distribtuion of charges.

(a) Which Gaussian surfaces have an electric flux of through them?

ANSWER:

Part B

(b) Which Gaussian surfaces have no electric flux through them?

ANSWER:

Conceptual Question 22.04

Part A

Consider a spherical Gaussian surface of radius centered at the origin. A charge is placed inside the sphere. To maximize the magnitude of the flux of the electric field through the Gaussian surface, the charge should be located

ANSWER:

+q/ϵ0

b

c

d

a

a

c

b

d

R Q

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Conceptual Question 22.09

Part A

An uncharged conductor has a hollow cavity inside of it. Within this cavity there is a charge of +10µC that does not touch the conductor. There are no other charges in the vicinity. Which statement about this conductor is true? (There may be more than one correct choice.)

ANSWER:

Conceptual Question 22.08

Part A

A charge is uniformly spread over one surface of a very large nonconducting square elastic sheet having sides of length . At a point that is 1.25 cm outside the sheet, the magnitude of the electric field due to the sheet is . If the sheet is now

stretched so that its sides have length 2 , what is the magnitude of the electric field at ?

ANSWER:

at = 0, = /2, = 0.x y R z

at = /2, = 0, = 0.x R y z

at = 0, = 0, = /2.x y z R

at the origin.

The charge can be located anywhere, since flux does not depend on the position of the charge as long as it is inside the sphere.

The inner surface of the conductor carries a charge of -10µC and its outer surface carries no excess charge.

The inner and outer surfaces of the conductor each contain charges of -5µC.

The net electric field within the material of the conductor points away from the +10µC charge.

The outer surface of the conductor contains +10µC of charge and the inner surface contains -10µC.

Both surfaces of the conductor carry no excess charge because the conductor is uncharged.

Q d P E

d P

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Prelecture Concept Question 22.06

Part A

Five point charges q and four Gaussian surfaces S are shown in the figure. What is the total electric flux through surface S2?

ANSWER:

4E

/2E

E

/4E

2E

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Prelecture Concept Question 22.05

Part A

Five point charges q and four Gaussian surfaces S are represented in the figure shown. Through which of the Gaussian surfaces are the total electric flux zero?

Check all that apply.

ANSWER:

zero

3q/εo

5q/εo

q/εo

2q/εo

4q/εo

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Problem 22.16

Part A

Electric charge is uniformly distributed inside a nonconducting sphere of radius 0.30 m. The electric field at a point , which is 0.50 m from the center of the sphere, is 15,000 N/C and is directed radially outward. What is the maximum magnitude of the electric field due to this sphere?

ANSWER:

Problem 22.23

Part A

A huge (essentially infinite) horizontal nonconducting sheet 10.0 cm thick has charge uniformly spread over both faces. The upper face carries +95.0 nC/m2 while the lower face carries -25.0 nC/ m2. What is the magnitude of the electric field at a point within the sheet 2.00 cm below the upper face? ( = 8.85 × 10-12 C2/N · m2)

ANSWER:

S2

S3

S4

S1

The total electric flux is not zero through any of the Gaussian surfaces.

P

36,000 N/C

42,000 N/C

48,000 N/C

30,000 N/C

25,000 N/C

ε0

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Problem 22.22

Part A

A very large sheet of a conductor carries a uniform charge density of 4.00 pC/mm2 on its surfaces. What is the electric field strength 3.00 mm outside the surface of the conductor? ( = 8.85 × 10-12 C2/N · m2)

ANSWER:

Problem 22.38

A long line carrying a uniform linear charge density runs parallel to and from the surface of a large, flat plastic sheet that has a uniform surface charge density of on one side.

Part A

Find the location of all points where an particle would feel no force due to this arrangement of charged objects.

ANSWER:

Part B

Choose an appropriate location of these points at a distance, calculated in part A.

0.00 N/C

1.36 × 104 N/C

7.91 × 103 N/C

3.95 × 103 N/C

6.78 × 103 N/C

ε0

9.04 × 105 N/C

4.52 × 105 N/C

2.26 × 105 N/C

0.226 N/C

0.452 N/C

+50.0 μC/m 10.0 cm −100 μC/m2

α

= from the line. L m

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ANSWER:

Score Summary: Your score on this assignment is 0.0%.

You received 0 out of a possible total of 20 points.

above the line

between the line and the sheet

11/30/2018 HW3

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HW3 Due: 11:59pm on Friday, October 5, 2018

You will receive no credit for items you complete after the assignment is due. Grading Policy

Exercise 23.10

Four electrons are located at the corners of a square 10.0 on a side, with an alpha particle at its midpoint.

Part A

How much work is done by the Coulomb force when the alpha particle moves to the midpoint of one of the sides of the square?

ANSWER:

Exercise 23.2

A point charge is held stationary at the origin. A second charge is placed at point , and the electric potential energy of the pair of charges is . When the second charge is moved to point , the electric force on the charge does

of work.

Part A

What is the electric potential energy of the pair of charges when the second charge is at point ?

Express your answer using two significant figures.

ANSWER:

Exercise 23.16

Two stationary point charges + 3.00 and + 2.00 are separated by a distance of 50.0 . An electron is released from rest at a point midway between the two charges and moves along the line connecting the two charges.

Part A

What is the speed of the electron when it is 10.0 from the + 3.00- charge?

ANSWER:

Exercise 23.39

nm

= W J

q1 q2 a

+5.4 × J10−8 b −1.9 × J10−8

b

J

nC nC cm

cm nC

= v m/s

11/30/2018 HW3

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The electric field at the surface of a charged, solid, copper sphere with radius 0.250 is 3500 , directed toward the center of the sphere. .

Part A

What is the potential at the center of the sphere, if we take the potential to be zero infinitely far from the sphere?

ANSWER:

Conceptual Question 23.01

Part A

If the electric field is zero everywhere inside a region of space, the potential must also be zero in that region.

ANSWER:

Conceptual Question 23.03

Part A

If the electrical potential in a region is constant, the electric field must be zero everywhere in that region.

ANSWER:

Conceptual Question 23.06

Part A

Suppose a region of space has a uniform electric field, directed towards the right, as shown in the figure. Which statement about the electric potential is true?

m N/C

= V V

True

False

True

False

11/30/2018 HW3

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ANSWER:

Conceptual Question 23.08

Part A

Suppose you have two point charges of opposite sign. As you move them farther and farther apart, the potential energy of this system relative to infinity

ANSWER:

Conceptual Question 23.13

Part A

A nonconducting sphere contains positive charge distributed uniformly throughout its volume. Which statements about the potential due to this sphere are true? All potentials are measured relative to infinity. (There may be more than one correct choice.)

Choose all that apply.

ANSWER:

The potential at points and are equal, and the potential at point is higher than the potential at point .A B C A

The potential at all three locations ( , , ) is the same because the field is uniform.A B C

The potential at point is the highest, the potential at point is the second highest, and the potential at point is the lowest.

A B C

The potential at points and are equal, and the potential at point is lower than the potential at point .A B C A

stays the same.

increases.

decreases.

11/30/2018 HW3

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Prelecture Concept Question 23.01

Part A

A positive charge moves in the direction of an electric field. Which of the following statements are true?

Check all that apply.

ANSWER:

Prelecture Concept Question 23.03

Part A

A positive charge is moved from point A to point B along an equipotential surface. How much work is performed or required in moving the charge?

ANSWER:

The potential at the surface is higher then the potential at the center.

The potential at the center of the sphere is zero.

The potential at the center of the sphere is the same as the potential at the surface.

The potential at the center is the same as the potential at infinity.

The potential is highest at the center of the sphere.

The potential energy associated with the charge decreases.

The electric field does positive work on the charge.

The potential energy associated with the charge increases.

The electric field does negative work on the charge.

The electric field does not do any work on the charge.

The amount of work done on the charge cannot be determined without additional information.

Work is both performed and required in moving the charge from point A to point B.

Work is required in moving the positive charge from point A to point B.

No work is performed or required in moving the positive charge from point A to point B.

Work is performed in moving the positive charge from point A to point B.

11/30/2018 HW3

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Prelecture Concept Question 23.06

Part A

Which of the following statements are true?

Check all that apply.

ANSWER:

Problem 23.06

Part A

A +4.0 μC-point charge and a -4.0-μC point charge are placed as shown in the figure. What is the potential difference, A - B, between points and ? ( = 1/4π = 8.99 × 109 N · m2/C2)

ANSWER:

An equipotential surface is a three-dimensional surface on which the electric potential is the same at every point.

Electric field lines and equipotential surfaces are always mutually perpendicular.

The potential energy of a test charge decreases as it moves along an equipotential surface.

When all charges are at rest, the surface of a conductor is always an equipotential surface.

The potential energy of a test charge increases as it moves along an equipotential surface.

V

V A B k ε0

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Problem 23.28

Part A

Two long conducting cylindrical shells are coaxial and have radii of 20 mm and 80 mm. The electric potential of the inner conductor, with respect to the outer conductor, is +600 V. What is the maximum electric field magnitude between the cylinders? ( = 1/4π = 8.99 × 109 N · m2/C2)

ANSWER:

Problem 23.37

Part A

In a certain region, the electric potential due to a charge distribution is given by the equation where x and y are measured in meters and is in volts. At which point is the electric field equal to zero?

ANSWER:

96 kV

48 kV

0.00 V

48 V

96 V

k ε0

10,000 V/m

18,000 V/m

22,000 V/m

26,000 V/m

14,000 V/m

V (x, y) = 2xy − − y,x2

V

11/30/2018 HW3

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Problem 24.66

A parallel-plate capacitor is made from two plates 12.0 on each side and 4.50 apart. Half of the space between these plates contains only air, but the other half is filled with Plexiglas of dielectric constant 3.40. (See the figure below.) An 18.0 battery is connected across the plates.

Part A

What is the capacitance of this combination?

ANSWER:

Part B

How much energy is stored in the capacitor?

ANSWER:

Part C

If we remove the Plexiglas, but change nothing else, how much energy will be stored in the capacitor?

ANSWER:

Problem 24.57

= 0.5 m, = 0.5 mx y

= 1 m, = 1 mx y

= 1 m, = 0.5 mx y

= 0.5 m, = 1 mx y

= 0 m, = 0 mx y

cm mm V

= C F

= U J

= U J

11/30/2018 HW3

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Three capacitors having capacitances of 9.0 , 8.0 , and 4.7 are connected in series across a 30- potential difference.

Part A

What is the charge on the 4.7 capacitor?

Express your answer using two significant figures.

ANSWER:

Part B

What is the total energy stored in all three capacitors?

Express your answer using two significant figures.

ANSWER:

Part C

The capacitors are disconnected from the potential difference without allowing them to discharge. They are then reconnected in parallel with each other, with the positively charged plates connected together. What is the voltage across each capacitor in the parallel combination?

Express your answer using two significant figures.

ANSWER:

Part D

What is the total energy now stored in the capacitors?

Express your answer using two significant figures.

ANSWER:

Problem 24.59

In the figure , each capacitance is 7.2 , and each capacitance is 4.8 .

μF μF μF V

μF

= Q3 C

= U J

= V V

= U J

C1 μF C2 μF

11/30/2018 HW3

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Part A

Compute the equivalent capacitance of the network between points a and b.

Express your answer using two significant figures.

ANSWER:

Part B

Compute the charge on the capacitor nearest to a when = 420 .

Express your answer using two significant figures.

ANSWER:

Part C

Compute the charge on the capacitor nearest to b when = 420 .

ANSWER:

Part D

Compute the charge on the capacitor nearest to a and b when = 420 .

Express your answer using two significant figures.

ANSWER:

= Ceq F

C1 Vab V

= Qa1 C

C1 Vab V

= Qb1 C

C2 Vab V

11/30/2018 HW3

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Part E

With 420 across a and b, compute .

Express your answer using two significant figures.

ANSWER:

Problem 24.51

For the capacitor network shown in the Figure , the potential difference across is 12.0 .

Part A

Find the total energy stored in this network.

ANSWER:

Part B

Find the energy stored in the 4.80- capacitor.

ANSWER:

Problem 24.35

= Q2 C

V Vcd

= Vcd V

ab V

= U μJ

μF

= U4.80 μF μJ

11/30/2018 HW3

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Part A

A parallel-plate capacitor consists of two parallel, square plates that have dimensions 1.0 cm by 1.0 cm. If the plates are separated by 5 mm, and the space between them is filled with teflon, what is the capacitance of this capacitor? (The dielectric constant for teflon is 2.1, and ε0 = 8.85 × 10-12 C2/N · m2.)

ANSWER:

Problem 24.32

Part A

A parallel-plate capacitor has a capacitance of 10 mF and is charged with a 20-V power supply. The power supply is then removed and a dielectric material of dielectric constant 4.0 is used to fill the space between the plates. What is the voltage now across the capacitor?

ANSWER:

Problem 24.29

Part A

Each plate of an air-filled parallel-plate air capacitor has an area of 0.0040 m2, and the separation of the plates is 0.080 mm. An electric field of 5.3 × 106 V/m is present between the plates. What is the energy density between the plates? ( = 8.85 × 10-12 C2/N · m2)

ANSWER:

0.37 pF

0.42 pF

0.18 pF

8.9×10−2 pF

5.0 V

80 V

20 V

2.5 V

10 V

ε0

11/30/2018 HW3

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Problem 24.24

Part A

A 8.00-μF parallel-plate capacitor has charges of 60.0 μC on its plates. How much potential energy is stored in this capacitor?

ANSWER:

Score Summary: Your score on this assignment is 0.0%.

You received 0 out of a possible total of 23 points.

210 J/m3

170 J/m3

84 J/m3

250 J/m3

124 J/m3

205 μJ

225 μJ

215 μJ

195 μJ

235 μJ

11/30/2018 HW1

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HW1 Due: 11:59pm on Friday, September 14, 2018

You will receive no credit for items you complete after the assignment is due. Grading Policy

Exercise 21.4

You have a pure (24-karat) gold ring with mass 10.8 . Gold has an atomic mass of 197 and an atomic number of 79.

Part A

How many protons are in the ring?

ANSWER:

Part B

What is their total positive charge?

Express your answer with the appropriate units.

ANSWER:

Part C

If the ring carries no net charge, how many electrons are in it?

ANSWER:

Exercise 21.6

Two small spheres spaced 20.0 apart have equal charge.

Part A

How many excess electrons must be present on each sphere if the magnitude of the force of repulsion between them is 3.33 10 ?

ANSWER:

Exercise 21.12

g g/mol

= np

= Q

= ne

cm

× −21 N

= ne

11/30/2018 HW1

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A negative charge of -0.510 exerts an upward 0.700- force on an unknown charge that is located 0.500 directly below the first charge.

Part A

What is the value of the unknown charge (magnitude and sign)?

Express your answer with the appropriate units.

ANSWER:

Part B

What is the magnitude of the force that the unknown charge exerts on the -0.510 charge?

Express your answer with the appropriate units.

ANSWER:

Part C

What is the direction of this force?

ANSWER:

Electric Field Conceptual Question

Part A

For the charge distribution provided, indicate the region (A to E) along the horizontal axis where a point exists at which the net electric field is zero.

If no such region exists on the horizontal axis choose the last option (nowhere).

μC N m

= q

μC

= F

upward

downward

11/30/2018 HW1

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You did not open hints for this part.

ANSWER:

Part B

For the charge distribution provided, indicate the region (A to E) along the horizontal axis where a point exists at which the net electric field is zero.

If no such region exists on the horizontal axis choose the last option (nowhere).

You did not open hints for this part.

ANSWER:

A

B

C

D

E

nowhere

11/30/2018 HW1

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Part C

For the charge distribution provided, indicate the region (A to E) along the horizontal axis where a point exists at which the net electric field is zero.

If no such region exists on the horizontal axis choose the last option (nowhere).

You did not open hints for this part.

ANSWER:

Part D

For the charge distribution provided, indicate the region (A to E) along the horizontal axis where a point exists at which the net electric field is zero.

A

B

C

D

E

nowhere

A

B

C

D

E

nowhere

11/30/2018 HW1

https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=6573925 5/9

You did not open hints for this part.

ANSWER:

Exercise 21.20

Two point charges are placed on the x-axis as follows: charge = 3.95 is located at 0.204 , and charge = 4.95 is at -0.295 .

Part A

What is the magnitude of the total force exerted by these two charges on a negative point charge = -5.99 that is placed at the origin?

ANSWER:

Part B

What is the direction of the total force exerted by these two charges on a negative point charge = -5.99 that is placed at the origin?

ANSWER:

A

B

C

D

E

Nowhere along the finite x axis

q1 nC x = m q2 nC x = m

q3 nC

= F N

q3 nC

11/30/2018 HW1

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Exercise 21.24

A particle has a charge of -5.55 .

Part A

Find the magnitude of the electric field due to this particle at a point 0.350 directly above it.

Express your answer with the appropriate units.

ANSWER:

Part B

Find the direction of this electric field.

ANSWER:

Part C

At what distance from this particle does its electric field have a magnitude of 14.0 ?

Express your answer with the appropriate units.

ANSWER:

Prelecture Concept Question 21.08

Part A

to the + directionx

to the - directionx

perpendicular to the -axisx

the force is zero

nC

m

= E

up, away from the particle

down, toward the particle

N/C

= L

11/30/2018 HW1

https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=6573925 7/9

The strength of the electric field at a certain distance from a point charge is represented by E. What is the strength of the electric field at twice the distance from the point charge?

ANSWER:

Prelecture Concept Question 21.10

Part A

When a point charge of +q is placed on one corner of a square, an electric field strength of 2 N/C is observed at the center of the square. Suppose three identical charges of +q are placed on the remaining three corners of the square. What is the magnitude of the net electric field at the center of the square?

ANSWER:

Prelecture Concept Question 21.04

Part A

Two charged objects are separated by some distance. The charge on the first object is greater than the charge on the second object. How does the force between the two objects compare?

ANSWER:

At twice the distance, the strength of the field is E/4.

At twice the distance, the strength of the field is E/2.

At twice the distance, the strength of the field is 4E.

At twice the distance, the strength of the field is 2E.

At twice the distance, the strength of the field remains equal to E.

The magnitude of the net electric field at the center of the square is 6 N/C.

The magnitude of the net electric field at the center of the square is 4 N/C.

The magnitude of the net electric field at the center of the square is 0 N/C.

The magnitude of the net electric field at the center of the square is 8 N/C.

The magnitude of the net electric field at the center of the square is 2 N/C.

11/30/2018 HW1

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Prelecture Concept Question 21.02

Part A

A positively charged rod is brought close to one end of an uncharged metal rod but does not actually touch it. What type of charge does the end of the metal rod closest to the positively charged rod acquire?

ANSWER:

Problem 21.01

Part A

A piece of plastic has a net charge of +2.00 μC. How many more protons than electrons does this piece of plastic have? (e = 1.60 × 10-19 C)

ANSWER:

The charged objects exert electrostatic forces on each other that are equal in magnitude and opposite in direction.

The first object exerts a large electrostatic force on the second object.

The charged objects exert electrostatic forces on each other that are equal in magnitude and pointing in the same direction.

The second object exerts a large electrostatic force on the first object.

The end of the metal rod closest to the positively charged rod remains neutral.

The end of the metal rod closest to the positively charged rod can acquire either a positive or negative charge, depending on the composition of the metal.

The end of the metal rod closest to the positively charged rod acquires a positive charge.

The end of the metal rod closest to the positively charged rod acquires a negative charge.

1.25 × 1019

2.50 × 1019

2.50 × 1013

1.25 × 1013

11/30/2018 HW1

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Problem 21.03

Part A

When two point charges are 2.0 cm apart, each one experiences a 1.0-N electric force due to the other charge. If they are moved to a new separation of 8.0 cm, the electric force on each of them is closest to

ANSWER:

Problem 21.06

Part A

Charge nC is at ( m, ), charge nC is at ( , m), and charge nC is at ( , ). What is the magnitude of the net electrostatic force on the -nC charge due to the other charges? (

N · m2/C2)

ANSWER:

Part B

What is the direction of the net electrostatic force on the -nC charge due to the other charges?

ANSWER:

Score Summary: Your score on this assignment is 0.0%.

You received 0 out of a possible total of 13 points.

1.0 N.

4.0 N.

16 N.

0.25 N.

0.063 N.

= 6.0Q1 0.30 0 = −1.0Q2 0 0.10 = 5.0Q3 0 0 5.0

k = 1/4 = 8.99 ×πϵ0 10 9

N

5.0

above -axis ∘ x

11/30/2018 HW6

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HW6 Due: 11:59pm on Saturday, November 10, 2018

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Exercise 27.12

A horizontal rectangular surface has dimensions 2.85 by 3.40 and is in a uniform magnetic field that is directed at an angle of 26.0 above the horizontal.

Part A

What must the magnitude of the magnetic field be to produce a flux of 3.20 10 through the surface?

Express your answer with the appropriate units.

ANSWER:

Exercise 27.22

In a cyclotron, the orbital radius of protons with energy 300 is 16.0 . You are redesigning the cyclotron to be used instead for alpha particles with energy 300 . An alpha particle has charge 2e and mass 6.64 10 .

Part A

If the magnetic field isn t changed, what will be the orbital radius of the alpha particles?

Express your answer to three significant figures and include the appropriate units.

ANSWER:

Exercise 27.28

Part A

What is the speed of a beam of electrons when the simultaneous influence of an electric field of and a magnetic field of , with both fields normal to the beam and to each other, produces no deflection of the electrons?

ANSWER:

Part B

When the electric field is removed, what is the radius of the electron orbit?

cm cm ∘

× −4 Wb

= B

keV cm keV q = + m = × kg−27

= Rα

1.56 × V/m104

4.62 × T10−3

= v m/s

11/30/2018 HW6

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ANSWER:

Part C

What is the period of the orbit?

ANSWER:

Exercise 27.36

An electromagnet produces a magnetic field of 0.590 in a cylindrical region of radius 2.90 between its poles. A straight wire carrying a current of 10.7 passes through the center of this region and is perpendicular to both the axis of the cylindrical region and the magnetic field.

Part A

What magnitude of force is exerted on the wire?

ANSWER:

Exercise 27.46

A coil with a magnetic moment of 1.50 is oriented initially with its magnetic moment antiparallel to a uniform magnetic field of magnitude 0.845 .

Part A

What is the change in potential energy of the coil when it is rotated 180 so that its magnetic moment is parallel to the field?

ANSWER:

Prelecture Concept Question 27.05

Part A

A charged particle enters into a uniform magnetic field such that its velocity vector is perpendicular to the magnetic field vector. Ignoring the particle's weight, what type of path will the particle follow?

ANSWER:

= R m

= T s

T cm A

= F N

A ⋅ m2

T

∘

= U J

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Conceptual Question 27.07

Part A

A vertical wire carries a current vertically upward in a region where the magnetic field vector points toward the north. What is the direction of the magnetic force on this current due to the field?

ANSWER:

Prelecture Concept Question 27.01

Part A

Which of the following statements are true?

Check all that apply.

ANSWER:

The charged particle will follow a circular path.

The charged particle will follow a straight-line path.

The charged particle will follow a parabolic path.

The charged particle will follow a spiral path.

downward

toward the north

toward the south

toward the west

toward the east

Scientists have evidence that single isolated magnetic poles, called magnetic monopoles, exist.

The north pole of a bar magnet will attract the south pole of another bar magnet.

Earth's geographic south pole is also a magnetic south pole.

The south poles of two bar magnets will repel each other.

Earth's geographic north pole is actually a magnetic south pole.

The north poles of two bar magnets will attract each other.

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Prelecture Concept Question 27.03

Part A

Consider a magnetic force acting on an electric charge in a uniform magnetic field. Which of the following statements are true?

Check all that apply.

ANSWER:

Conceptual Question 27.05

Part A

Ions having equal charges but masses of and 2 are accelerated through the same potential difference and then enter a uniform magnetic field perpendicular to their path. If the heavier ions follow a circular arc of radius , what is the radius of the arc followed by the lighter?

ANSWER:

Conceptual Question 27.01

The direction of the magnetic force acting on a moving charge in a magnetic field is perpendicular to the direction of the magnetic field.

A magnetic force is exerted on a stationary electric charge in a uniform magnetic field.

A magnetic force is exerted on an electric charge moving through a uniform magnetic field.

An electric charge moving parallel to a magnetic field experiences a magnetic force.

The direction of the magnetic force acting on a moving electric charge in a magnetic field is perpendicular to the direction of motion.

An electric charge moving perpendicular to a magnetic field experiences a magnetic force.

M M R

3R

/R 2√

4R

2√ R

/2R

11/30/2018 HW6

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Part A

An electron moving in the direction of the + -axis enters a magnetic field. If the electron experiences a magnetic deflection in the - direction, the direction of the magnetic field in this region points in the direction of the

ANSWER:

Problem 27.24

Part A

A straight 15.0-g wire that is 2.00 m long carries a current of 8.00 A. This wire is aligned horizontally along the west-east direction with the current going from west to east. You want to support the wire against gravity using the weakest possible uniform external magnetic field.

(a) Which way should the magnetic field point?

ANSWER:

Part B

(b) What is the magnitude of the weakest possible magnetic field you could use?

ANSWER:

Score Summary: Your score on this assignment is 0.0%.

You received 0 out of a possible total of 12 points.

x y

- -axis.x

+z-axis.

- -axis.z

+y-axis.

- -axis.y

from east to west

from west to east

from south to north

from north to south

none of the above

T

11/30/2018 HW4

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HW4 Due: 11:59pm on Thursday, October 25, 2018

You will receive no credit for items you complete after the assignment is due. Grading Policy

Exercise 25.16

Part A

A ductile metal wire has resistance . What will be the resistance of this wire in terms of if it is stretched to three times its original length, assuming that the density and resistivity of the material do not change when the wire is stretched. (Hint: The amount of metal does not change, so stretching out the wire will affect its cross-sectional area.)

ANSWER:

Conceptual Question 25.01

Part A

The figure shows a steady electric current passing through a wire with a narrow region. What happens to the drift velocity of the moving charges as they go from region to region and then to region ?

ANSWER:

Conceptual Question 25.03

Part A

R R

= R1 R

A B C

The drift velocity increases all the time.

The drift velocity decreases all the time.

The drift velocity remains constant.

The drift velocity increases from A to B and decreases from B to C.

The drift velocity decreases from A to B and increases from B to C.

11/30/2018 HW4

https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=6872436 2/8

The figure shows two connected wires that are made of the same material. The current entering the wire on the left is 2.0 A and in that wire the electron drift speed is d. What is the electron drift speed in the wire on the right side?

ANSWER:

Conceptual Question 25.10

Part A

Two cables of the same length are made of the same material, except that one cable has twice the diameter of the other cable. When the same potential difference is maintained across both cables, which of the following statements are true? (There may be more than one correct choice.)

Choose all that apply.

ANSWER:

Prelecture Concept Question 25.01

Part A

Which of the following statements are true?

v

dv

4 dv

d/2v

2 dv

d/4v

Both cables carry the same current density.

The electrons have the same drift velocity in both cables.

The current in the thin cable is four times as great as the current in the thick cable.

The same current flows through both cables.

The current in the thin cable is twice as great as the current in the thick cable.

11/30/2018 HW4

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Check all that apply.

ANSWER:

Prelecture Concept Question 25.05

Part A

Consider two copper wires with the same cross-sectional area. Wire A is twice as long as wire B. How do the resistivities and resistances of the two wires compare?

Check all that apply.

ANSWER:

Prelecture Concept Question 25.09

Part A

A circuit maintains a constant resistance. If the current in the circuit is doubled, what is the effect on the power dissipated by the circuit?

ANSWER:

A battery does work on electric charges to bring them to a position of higher electric potential energy so that they can flow through a circuit to a lower potential energy.

The potential difference between the terminals of a battery, when no current flows to an external circuit, is referred to as the terminal voltage.

The internal resistance of a battery decreases with decreasing temperature.

A battery is a device that produces electricity by transforming chemical energy into electrical energy.

Wire A has twice the resistance of wire B.

Wire B has twice the resistance of wire A.

Wire A and wire B have the same resistance.

Wire A and wire B have the same resistivity.

Wire B has twice the resistivity of wire A.

Wire A has twice the resistivity of wire B.

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Problem 25.16

Part A

The resistivity of gold is 2.44×10-8 Ω•m at room temperature. A gold wire that is 1.4 mm in diameter and 39 cm long carries a current of 950 mA. What is the electric field in the wire?

ANSWER:

Problem 25.24

Part A

A Nichrome wire is used as a heating element in a toaster. From the moment the toaster is first turned on to the moment the wire reaches it maximum temperature, the current in the wire drops by 20.0% from its initial value. What is the temperature change in the wire? The temperature coefficient of resistivity for Nichrome is 0.000400 (°C)-1.

ANSWER:

The power dissipated is reduced by a factor of 2.

The power dissipated remains constant.

The power dissipated is doubled.

The power dissipated is reduced by a factor of 4.

The power dissipated is quadrupled.

3.8×10−3 V/m

1.2×10−2 V/m

1.5×10−2 V/m

1.9×10−2 V/m

3.8×10−2 V/m

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Problem 25.26

Part A

A piece of wire 41.5 cm long carries a current I when a voltage V is applied across its ends at a temperature of 0°C. If the resistivity of the material of which the wire is made varies with temperature as shown in the graph in the figure, what length of the same diameter wire is needed so that the same current flows when the same voltage is applied at temperature 400°C?

ANSWER:

Problem 25.29

Part A

When a voltage difference is applied to a piece of metal wire, a 4-mA current flows through it. If this metal wire is now replaced with a silver wire having twice the diameter of the original wire, how much current will flow through the silver wire? The lengths of both wires are the same, and the voltage difference remains unchanged. (The resistivity of the original metal is 1.68 × 10-8 Ω · m, and the resistivity of silver is 1.59 × 10-8 Ω · m.)

ANSWER:

625°C

200°C

300°C

400°C

500°C

cm

11/30/2018 HW4

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Problem 25.38

Part A

The voltage and power ratings of a particular light bulb, which are its normal operating values, are 110 V and 60 W. Assume the resistance of the filament of the bulb is constant and is independent of operating conditions. If the light bulb is operated with a current that is 50% of the current rating of the bulb, what is the actual power drawn by the bulb?

ANSWER:

Problem 25.44

Part A

In the figure a current of 6.0 A is drawn from the battery. What is the terminal voltage Vab of the battery?

ANSWER:

17 mA

8.5 mA

15 mA

4.2 mA

30 W

20 W

10 W

25 W

15 W

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Problem 25.56

A heating element made of tungsten wire is connected to a large battery that has negligible internal resistance. When the heating element reaches 80.0 , it consumes electrical energy at a rate of 420 . Assume that the temperature coefficient of resistivity has the value given in Table 25.2 in the textbook and that it is constant over the temperature range in this problem. In the equation

take to be 20.0 .

Part A

What is its power consumption when the temperature of the heating element is 110.0 ?

Express your answer to two significant figures and include the appropriate units.

ANSWER:

Problem 25.58

A resistor with resistance is connected to a battery that has emf 16.0 and internal resistance = 0.350 .

Part A

For what two values of will the power dissipated in the resistor be 78.0 ?

Enter your answers separated by a comma.

ANSWER:

Problem 25.70

Compact fluorescent bulbs are much more efficient at producing light than are ordinary incandescent bulbs. They initially cost much more, but last far longer and use much less electricity. According to one study of these bulbs, a compact bulb that produces as much light as a 100 incandescent bulb uses only 23.0 of power. The compact bulb lasts 1.00×104 hours, on

0.00 V

-24 V

+24 V

+12 V

-12 V

C∘ W

R(T ) = [1 + α(T − )]R0 T0

T0 C ∘

C∘

= P

R V r Ω

R W

, = R1 R2 Ω

W W

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the average, and costs 12.0 , whereas the incandescent bulb costs only 74.0 ¢, but lasts just 750 hours. The study assumed that electricity cost 7.00 ¢ per and that the bulbs were on for 4.0 per day.

Part A

What is the total cost (including the price of the bulbs) to run incandescent bulbs for 3.0 years?

ANSWER:

Part B

What is the total cost (including the price of the bulbs) to run compact fluorescent bulbs for 3.0 years?

ANSWER:

Part C

How much do you save over 3.0 years if you use a compact fluorescent bulb instead of an incandescent bulb?

ANSWER:

Part D

What is the resistance of a "100 " fluorescent bulb? (Remember, it actually uses only 23 of power and operates across 120 .)

ANSWER:

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$ kWh h

dollar(s)

dollar(s)

dollar(s)

W W V

= R Ω

11/30/2018 HW5

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HW5 Due: 11:59pm on Friday, November 2, 2018

You will receive no credit for items you complete after the assignment is due. Grading Policy

Exercise 26.2

A machine part has a resistor protruding from an opening in the side. This resistor is connected to three other resistors, as shown in the figure . An ohmmeter connected across and reads 2.00 .

Part A

What is the resistance of ?

Express your answer in ohms to two significant figures.

ANSWER:

Exercise 26.12

In the battery has emf 43.0 and negligible internal resistance. = 6.00 . The current through is 2.50 and the current

through = 5.10 .

X a b

Ω

X

= X Ω

V

R1 Ω R1 A R3 A

11/30/2018 HW5

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Part A

What is the resistance ?

Express your answer with the appropriate units.

ANSWER:

Part B

What is the resistance ?

Express your answer with the appropriate units.

ANSWER:

Exercise 26.24

The batteries shown in the circuit in the figure have negligibly small internal resistances.

Part A

Find the current through the 30.0 resistor.

ANSWER:

Part B

Find the current through the 20.0 resistor.

ANSWER:

R2

= R2

R3

= R3

Ω

= I A

Ω

11/30/2018 HW5

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Part C

Find the current through the 10.0 battery.

ANSWER:

Exercise 26.30

The 5.00- battery in is removed from the circuit and replaced by a 15.00- battery, with its negative terminal next to point . The rest of the circuit is as shown in the figure.

Part A

Find the current in the upper branch.

Express your answer with the appropriate units. Enter positive value if the current is to the left and negative value if the the current is to the right.

ANSWER:

Part B

Find the current in the middle branch.

Express your answer with the appropriate units. Enter positive value if the current is to the left and negative value if the the current is to the right.

ANSWER:

= I A

V

= I A

V

V b

= I

= I

11/30/2018 HW5

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Part C

Find the current in the lower branch.

Express your answer with the appropriate units. Enter positive value if the current is to the left and negative value if the the current is to the right.

ANSWER:

Part D

Find the potential difference of point relative to point .

Express your answer with the appropriate units.

ANSWER:

Exercise 26.32

In the circuit shown in the figure both batteries have insignificant internal resistance and the idealized ammeter reads 2.00 in the direction shown.

Part A

Find the emf of the battery.

ANSWER:

Part B

= I

Vab a b

= Vab

A

E

= E V

11/30/2018 HW5

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Is the polarity shown correct?

ANSWER:

RC Circuit and Current Conceptual Question

In the diagram below,the two resistors, and , are identical and the capacitor is initially uncharged with the switch open.

Part A

How does the current through compare with the current through immediately after the switch is first closed?

You did not open hints for this part.

ANSWER:

Part B

How does the current through compare with the current through a very long time after the switch has been closed?

You did not open hints for this part.

ANSWER:

yes

no

R1 R2

R1 R2

The current through the current through .R1

is greater than

is less than

is equal to

R2

R1 R2

11/30/2018 HW5

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Part C

How does the current through compare with the current through immediately after the switch is opened (after being closed a very long time)?

You did not open hints for this part.

ANSWER:

Exercise 26.50

A 16.0- capacitor is charged to a potential of 50.0 and then discharged through a 265- resistor.

Part A

How long does it take the capacitor to lose half of its charge?

Express your answer with the appropriate units.

ANSWER:

Part B

How long does it take the capacitor to lose half of its stored energy?

Express your answer with the appropriate units.

ANSWER:

Exercise 26.48

The current through the current through .R1

is greater than

is less than

is equal to

R2

R1 R2

The current through the current through .R1

is greater than

is less than

is equal to

R2

μF V Ω

= t

= t

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A 1.70- capacitor is charging through a 14.0- resistor using a 12.0- battery.

Part A

What will be the current when the capacitor has acquired 1/4 of its maximum charge?

ANSWER:

Part B

Will it be 1/4 of the maximum current?

ANSWER:

Exercise 26.46

A resistor and capacitor are connected in series to an emf source. The time constant for the circuit is 0.780 .

Part A

A second capacitor, identical to the first, is added in series. What is the time constant for this new circuit?

Express your answer with the appropriate units.

ANSWER:

Part B

In the original circuit a second capacitor, identical to the first, is connected in parallel with the first capacitor. What is the time constant for this new circuit?

Express your answer with the appropriate units.

ANSWER:

Problem 26.38

μF Ω V

= I A

yes

no

s

= τ

= τ

11/30/2018 HW5

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Part A

A 4.0-μF capacitor that is initially uncharged is connected in series with a 4.0-k resistor and an ideal 17.0-V battery. How much energy is stored in the capacitor 17 ms after the battery has been connected?

ANSWER:

Problem 26.57

Part A

Find the potential of point with respect to point in the figure .

Express your answer using two significant figures.

ANSWER:

Part B

If points and are connected by a wire with negligible resistance, find the magnitude of the current in the 10.0 battery.

Express your answer using two significant figures.

ANSWER:

Ω

890 nJ

15,000 kJ

25 µJ

250,000 nJ

a b

= Vab V

a b V

= I A

11/30/2018 HW5

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Problem 26.69

A resistor consumes electrical power when connected to an emf . When resistor is connected to the same emf, it consumes electrical power .

Part A

In terms of and , what is the total electrical power consumed when they are both connected to this emf source in parallel?

ANSWER:

Part B

In terms of and , what is the total electrical power consumed when they are both connected to this emf source in series?

ANSWER:

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R1 P1 E R2 P2

P1 P2

= Ptot

P1 P2

= Ptot