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Question details

M 2d??????? di K

In this problem, you will be asked to calculate the magnetic field due to a set of two wires with antiparallel currents as shown in the diagram (Figure 1) . Each of the wires carries a current of magnitude I. The current in wire 1 is directed out of the page and that in wire 2 is directed into the page. The distance between the wires is 2d. The x axis is perpendicular to the line connecting the wires and is equidistant from the wires.

As you answer the questions posed here, try to look for a pattern in your answers.

Part A

Which of the vectors best represents the direction of the magnetic field created at point K (see the diagram in the problem introduction) by wire 1 alone?

Enter the number of the vector with the appropriate direction.The figure represents 8 radiant arrows, labeled 1 to 8, coming from the common center, with their tips forming a right octahedron. Arrow 1 is directed vertically upwards, and other arrows are numbered clockwise.

3

Correct

Part B

Which of the vectors best represents the direction of the magnetic field created at point K by wire 2 alone?

Enter the number of the vector with the appropriate direction.The figure represents 8 radiant arrows, labeled 1 to 8, coming from the common center, with their tips forming a right octahedron. Arrow 1 is directed vertically upwards, and other arrows are numbered clockwise.

3

Correct

Part C

Which of these vectors best represents the direction of the net magnetic field created at point K by both wires?

Enter the number of the vector with the appropriate direction.The figure represents 8 radiant arrows, labeled 1 to 8, coming from the common center, with their tips forming a right octahedron. Arrow 1 is directed vertically upwards, and other arrows are numbered clockwise.

3

Correct

Part D

Find the magnitude of the magnetic field B1K created at point K by wire 1.

Express your answer in terms of I, d, and appropriate constants.

B1K =

I?02?d

Correct

Of course, B2K=B1K because point K is equidistant from the wires.

Part E

Find the magnitude of the net magnetic field BK created at point K by both wires.

Express your answer in terms of I, d, and appropriate constants.

BK =

I?0?d

Correct

This result is fairly obvious because of the symmetry of the problem: At point K, the two wires each contribute equally to the magnetic field. At points L and M you should also consider the symmetry of the problem. However, be careful! The vectors will add up in a more complex way.

Part F

Point L is located a distance d2? from the midpoint between the two wires. Find the magnitude of the magnetic field B1L created at point L by wire 1.

Express your answer in terms of I, d, and appropriate constants.

B1L =

I?02?d3?

Correct

Part G

Point L is located a distance d2? from the midpoint between the two wires. Find the magnitude of the net magnetic field BL created at point L by both wires.

Express your answer in terms of I, d, and appropriate constants.

BL =

I?03?d

Correct

Part H

Point M is located a distance 2d from the midpoint between the two wires. Find the magnitude of the magnetic field B1M created at point M by wire 1.

Express your answer in terms of I, d, and appropriate constants.

B1M=

Part I

Find the magnitude of the net magnetic field BM created at point M by both wires.

Express your answer in terms of I, d, and appropriate constants.

BM=
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