Magnetic field from two wires mastering physics solutions

11/30/2018 HW7

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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

11/30/2018 HW7

https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=6923433 4/16

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

https://session.masteringphysics.com/myct/assignmentPrintView?displayMode=studentView&assignmentID=6923433 6/16

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