Direction of the magnetic field due to a wire conceptual question

11/30/2018 HW7

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

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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

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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

11/30/2018 HW7

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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)

11/30/2018 HW7

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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

11/30/2018 HW7

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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

11/30/2018 HW7

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ANSWER:

11/30/2018 HW7

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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

11/30/2018 HW7

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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.

11/30/2018 HW7

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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

11/30/2018 HW7

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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.

11/30/2018 HW7

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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

11/30/2018 HW7

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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

11/30/2018 HW7

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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:

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BC cm P

DA cm P CD AB

cm

P A

= B

into the page

out of the page