Question

An infinitely long wire carrying a 25-A current in a the positive x-direction is places along the xaxis in the vicinity of a 20-turn circular loop located in the x-y plane. If the magnetic field at the center of the loop is zero, what is the direction and magnitude of the current flowing in the loop

Answer 1

Answer:

0.2 A, clockwise direction

Explanation:

We are given that

Current,I=25 A

Number of turns=n=20

Magnetic field at center of r the loop=B=0

d=2 m

We have to find the direction and magnitude of current flowing in the loop.

Magnetic field due to current I

$B=\frac{\mu_0 I}{2\pi d}\hat{z}$

Magnetic field due to I'

$B'=-\frac{\mu_0 nI''}{2a}\hat{z}$

a=1 m

Net magnetic is zero

Therefore, $B+B'=0$

$\frac{\mu_0 I}{2\pi d}\hat{z}-\frac{\mu_0 nI''}{2a}\hat{z}=0$

$\frac{\mu_0 I}{2\pi d}\hat{z}=\frac{\mu_0 nI''}{2a}\hat{z}$

$\frac{I}{\pi d}=\frac{I'n}{a}$

$I'=\frac{aI}{\pi d n}=\frac{25\times 1}{3.14\times 2\times 20}=0.2 A$

Where $\pi=3.14$

Direction: Clockwise