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

Question

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Two round concentric metal wires lie on a tabletop, one inside the other. The inner wire has a diameter of 21.0cm and carries a clockwise current of 20.0A, as viewed from above, and the outer wire has a diameter of 30.0cm. 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? Please Choose The current's direction must be clockwise. The current's direction must be counterclockwise. 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

From right hand rule, since the current is clockwise in the inner wire, so while the fingers curl clockwise, the thumb will point downward , so the direction of magnetic field due to inner wire at the centre is downwards( inside the plane ).. so the current in the outerwire should be such that the field (thumb) is upwards. so when the thumb is upwards, the fingers can curl counterclockwise.. so the counterclokwise flow of current makes the thumb pointing upwards.

now Bdue to inner wire at centre = u*i / 2*pi*R1 = u*(20) / 2*pi*(21/2)

this should be equal to the magnitude of field due to outer wire

so

u*(20) / 2*pi*(21/2) = u*i / 2*pi*(30/2)

so i = 20x30 / 21 = 28.57 Ampere

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