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Loop A of radius rgtgtR moves toward loo...

Loop `A` of radius `rgtgtR` moves toward loop `B` with a constant velocity `V` such a way that their planes are always parallel. What is the distance between the two loops `(x)` when the induced emf in loop `A` is maximum?

A

`R`

B

`R/sqrt2`

C

`R/2`

D

`R(1-1sqrt2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`phi_(A)=(mu_(0)ipiR^(2))/(2pi(R^(2)+x^(2))^(3//2))pir^(2)`
`E_(A)=-(dphi)/(dt)=(mu_(0)ipi)/2R^(2)r^(2)(-3//2)(R^(2)+x^(2))^(5//2)2x(v)`
`E_(A)` is maximum when `(dE_(A))/(dx)=0`
`rArr d/(dx)x/(R^(2)+x^(2))^(5//2)=0`
or `(R^(2)+x^(2))^(-5//2)-(5x)/2(R^(2)+x^(2))^(3//2)` 2x=0 or `R^(2)+x^(2)-5 x^(2)=0`
or `x=R/2`
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