Two round concentric metal wires lie on a tabletop. one inside the other. The in

Question

Two round concentric metal wires lie on a tabletop. one inside the other. The inner wire has a diameter of 19.0 cm and carries a clockwise current of 16.0 A. as viewed from above, and the outer wire has a diameter of 36.0 cm. What must be the direction (as viewed from above) of the current in the outer wire so that the net magnetic field due to this combination of wires is zero at the common center of the wires? What must be the magnitude of the current in the outer wire so that the net magnetic field due to this combination of wires is zero at the common center of the wires?

Explanation / Answer

(a)
Using Right hand thumb rule,
As the inner wire carries Clockwise current, It will produce Magnetic Field with direction Into the page , to counter this effect, The outer wire needs to carry current in Anti clockwise Direction.

(b)
Magnetic Field at the center of a loop is given by, B = (uo * I) / (2*R)
Now For Net Magnetic Field = 0 ,
Binner = Bouter
(uo * Iinner) / (2*Rinner) = (uo * Iouter) / (2*Router)
16.0/ (19.0/2) = Iouter / (36/2)
Iouter =  30.3 A
Current in the outer wire, Iouter =  30.3 A

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