Two circular concentric metal wires lie on a tabletop, one inside the other. The

Question

Two circular concentric metal wires lie on a tabletop, one inside the other. The inner wire has a diameter of 18.0 cm and carries a clockwise current of 16.0 A, as viewed from above, and the outer wire has a diameter of 38.0 cm If the current in the outer wire was the same in magnitude as the current in the inner wire, but in the opposite direction, what would be the magnitude of the magnetic field due to these wires at their common center? In what direction (with respect to the tabletop) is the magnetic field found in previous step? upward, clockwise, counterclockwise, or downward.

Explanation / Answer

given

r1 = 18/2 = 9cm

r2 = 38cm/2 = 19cm

i1 =16 A

B1 = uo*i1/2*r1

B2 = uo*i2/2*r2

Bnet = B1+B2

Bnet = uo*i1/2*r1 + uo*i2/2*r2

given that i2 = -i1 so

Bnet = uo*i1*(1/r1 -1/r2)

Bnet =4*3.14*10-7 * 16*(1/0.09 - 1/0.19)

direction is clockwise .

Bnet = 1.17*10-4 T

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