Two round 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 10.0 A, as viewed from above, and the outer wire has a diameter of 30.0 cm. What must be the magnitude and 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?

Explanation:

The wires are in circular shape . They have common center .

magnetic field due to circular wire is given by the formula

B =

 where I is current , r is radius of the coil .

magnetic field due to inner wire

=

magnetic field due to outer wire

=

These should be equal  and opposite so that by cancelling each other , they create zero field.

 =

I = 16.66  A

Direction of current should be in opposite direction ie anticlockwise when looking from above.

find the sum of the two horizontal vectors and the sum of the two vertical vectors

isoceles right angled triangle