Question

A circular loop of radius R1 lies in the x − y plane, centered on the origin, and has a current i running through it clockwise when viewed from the positive z direction. A second loop with radius R2 sits above the first, centered on the positive z axis and parallel to the first.

1. If the second loop is centered at the point z = R1, what must the current be (direction and magnitude) in order for the net magnetic field at the center of the second loop to be zero.

2. If the second loop is centered at the point z = R1, what must the current be (direction and magnitude) in order for the net magnetic field at the center of the first loop to be zero.

Answer 1

Direction of magnetic field is given by right hand thumb rule, the thumb pointing towards the magnetic field

(1)

Direction of magnetic field of 1st loop is in -Z direection[ Using right hand thumb rule]

So , magnetic field in 2nd loop must be in +Z => current in loop 2 must be counterclockwise

(2)

Direction of magnetic field of 1st loop is in -Z direection[ Using right hand thumb rule]

So , magnetic field in 2nd loop must be in +Z => current in loop 2 must be counterclockwise