A current i_L flows in the counterclockwise direction in n circular loop of wire

Question

A current i_L flows in the counterclockwise direction in n circular loop of wire. A long straight wire lies a perpendicular distance 2R below the center of the circular loop of wire (see figure below). This long straight wire carries a different current i_w. (a) What is the direction of the magnetic field at the centre of the loop due to the current flowing in the loop? (b) What magnitude of current passing through the long straight wire is necessary to produce a net magnetic field of zero at the centre of the loop? (Write your answer in terms of iL.) (c) Should the current in the long straight wire flow to the right or to the left?

Explanation / Answer

a)Countercloskwise at the center of the loop using right hand thumb rule.

b)Bnet-center = Bloop + Wwire = 0

u0 iL/ 2 R - u0 iW/ 2 pi 2R = 0

u0 iL/ 2R = u0 iW/ 2 pi 2R

iW = 2 pi iL

Hence, iW = (2 pi ) iL

c)The current should flow in the left in order to get the B field zero at the center of the loop.

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