The figure below shows three long straight wires that are perpendicular to the p

ID: 2121554 • Letter: T

Question

The figure below shows three long straight wires that are perpendicular to the page. The

cross sections of the wires lie at the corners of a square. The currents in wires 1 and 2 are

into the page and have a magnitude i. The length of each side of the square is d. The

positive x direction is to the left, the positive y direction is upward, and the positive z

direction is out of the page. The net magnetic field at the empty corner is zero. Our goal

in this problem is to find the current in wire 3.

a. Let and be the magnetic field produced by wires 1 and 2, respectively.

Determine the direction of and at the empty corner. Draw the vectors in the

figure above and label them.

b. In unit vector notation, determine at the empty corner. Put you answer in

terms of i, d, and physical constants.

c. Using your answer from part b, find the direction of the current in the third wire.

Remember that the net magnetic field produced by all three wires is zero at the

empty corner. Explain your answer.

d. Determine the magnitude of the current i3 in wire 3. Put your answer in terms of i.