Question

Review Interactive Solution 21.61 for one approach to this problem. Two circular coils are concentric and lie in the same plane. The inner coil contains 180 turns of wire, has a radius of 0.011 m, and carries a current of 7.1 A. The outer coil contains 140 turns and has a radius of 0.021 m. What must be the magnitude of the current in the outer coil, such that the net magnetic field at the common center of the two coils is zero

Answer 1

Explanation:

To find the current in the outer coil, so the arrangement will be:

$X_{i}$ = $X_{0}$

therefore

$\frac{u_{0}I_{i}N_{i} }{2R_{i} }$ = $\frac{u_{0}I_{0}N_{0} }{2R_{0} }$

cross multiply to find $I_{0}$

$I_{0}$ = $I_{1}$ ($\frac{N_{i} }{N_{0} }$) ($\frac{R_{0} }{R_{i} }$)

   =7.1 (180/140)(0.021/0.011)

   $I_{0}$ = 17.4A

For the two magnet to have opposite direction, so the current in the outer coil definitely that current must have an opposite direction to that current(in the outer coil.