Need help with this problem. Answer is provided, just need it worked out and exp

Question

Need help with this problem. Answer is provided, just need it worked out and explained. Thanks.

1. Two long parallel wires carry equal currents, I, in opposite directions as shown. Midway between the wires in the same plane is acurrent loop ofradius R carrying a currentl as shown. AR A. (20 pts) Find the magnitude and direction ofthe magneticfield atthe center oftheloop due to all parts of the system. Ans. 0.43 mT out of the page B. (5 pts) What is the magnetic moment, m, ofthe current loop? Ans. 0.39 A m

Explanation / Answer

Here ,

I = 50 A

R = 5 cm = 0.05 m

for the magnetic field at the centre

magnetic field = u0 * I/(2R) + u0 * I/(2R) - u0 * I/(2R)

magnetic field = u0 * I/(2R)

magnetic field = 4pi *10^-7 * 50/(2 * 0.05)

magnetic field = 6.283 *10^-4 T

the magnetic field at the midpoint is 6.283 *10^-4 T

B)

magenetic moment of the current loop = N * I * A

magenetic moment of the current loop = 1 * 50 * pi * 0.05^2

magenetic moment of the current loop = 0.393 A.m^2

the magenetic moment of the current loop is 0.393 A.m^2

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