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

0.2 A, clockwise direction

Step-by-step 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=(\mu_0 I)/(2\pi d)\hat{z}`

Magnetic field due to I'

`B'=-(\mu_0 nI'')/(2a)\hat{z}`

a=1 m

Net magnetic is zero

Therefore,
`B+B'=0`

`(\mu_0 I)/(2\pi d)\hat{z}-(\mu_0 nI'')/(2a)\hat{z}=0`

`(\mu_0 I)/(2\pi d)\hat{z}=(\mu_0 nI'')/(2a)\hat{z}`

`(I)/(\pi d)=(I'n)/(a)`

`I'=(aI)/(\pi d n)=(25* 1)/(3.14* 2* 20)=0.2 A`

Where
`\pi=3.14`

Direction: Clockwise