Four wires, each carrying current I , are at the corners of a square (of size d

Question

Four wires, each carrying current I , are at the corners of a square (of size d ), as shown below.

Part A

What direction is the total magnetic field at the dot in the center?

Part B

What is the magnitude of the magnetic field at the dot from a single wire?  

Express your answer symbolically, using constants such as mu0 .

Part C

What is the magnitude of the total magnetic field from all the wires?

Express your answer symbolically. You should be able to evaluate any trig functions that you find.

Part D

Now a wire is placed on the dot, with a current going into the page. What direction is the force on this wire?

Part E

If this wire carries a current  I2 and has length L , what is the total force on this wire?

Explanation / Answer

A) upwards

B) distance from center to each corner,

r = sqrt(2)*d/2

magnetic field due to one wire, B = mue*I/(2*pi*sqrt(2)*d/2)

= mue*I/(pi*sqrt(2)*d)

C)

magnetic field duw to 4 wires, Bnet = 2*sqrt(2)*mue*I/(2*pi*sqrt(2)*d/2)

= 2*mue*I/(pi*d)

D) Left

E) F = Bnet*I2*L*sin(90)

= 2*mue*I*I2*L/(pi*d)

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