Loop A of radius r << R moves towards loop B with a constant velocity V in such a way that their planes are always parallel....

Q. Loop A of radius r << R moves towards loop B with a constant velocity V in 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/√2

(c) R/2

(d) R(1- 1/√2)

Ans: (c)

Sol: Magnetic flux associated with loop A is φ = BS

$ \displaystyle \phi = \frac{\mu_0}{4\pi} \frac{2\pi i R^2}{(R^2 +x^2 )^{3/2}}(\pi r^2)$

Induced emf in loop A is

$ \displaystyle e = -\frac{d \phi}{dt} $

$ \displaystyle e = -\frac{d}{dt}(\frac{\mu_0}{4\pi} \frac{2\pi i R^2}{(R^2 +x^2 )^{3/2}}(\pi r^2)) $

For e to be maximum $\displaystyle \frac{de}{dx} = 0 $