Question

A conventional current of 7 A runs clockwise in a circular loop of wire in the xy plane, with center at the origin and with radius 0.097 m. Another circular loop of wire lies in the same plane, with its center at the origin and with radius 0.03 m. How much conventional current must run counterclockwise in this smaller loop in order for the magnetic field at the origin to be zero?

Answer 1

2.17 A

Step-by-step explanation:

The magnetic field due to a circular current carrying coil is given by

B = k x 2i / r

For i = 7 A, r = 0.097 m, clockwise

B = k x 2 x 7 / 0.097 = 144.33 k (inwards)

The direction of magnetic field is given by the Maxwell's right hand thumb rule.

The magnetic field is same but in outwards direction as the current is in counter clockwise direction. Let the current be i.

Now, r = 0.03 m, B = 144.33 K, i = ?

B = k x 2i / r

144.33 K = K x 2 x i / 0.03

i = 2.17 A