Question

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. $\frac{R}{\sqrt{2}}$
• C. $\frac{R}{2}$
• D. $R⟮1-\frac{1}{\sqrt{2}}⟯$

Answer 1

Answer: (C)

$\frac{R}{2}$

Here,

Loop A of Radius r moves towards loop B or radius R with a constant velocity V.

Their planes are always parallel.
We know,

${\Phi }_A=\left[\frac{M_{0}i\pi R^2}{2\pi (R^2+x^2{)}^{3/2}}\right]\pi r^2$

$E_A=-\frac{d\Phi }{dt}=\frac{M_{0}i\pi }{2}\left(\frac{-3}{2}\right)(R^2+x^2{)}^{-5/2}.2x(v)$

$E_A$ is maximum when $\frac{dEA}{dx}=0$

$=\frac{d}{dx}\frac{x}{(R^2+x^2{)}^{5/2}}=0$

$(R^2+x^2{)}^{5/2}=\frac{5x}{2}(R^2+x^2{)}^{3/2}2x=0$

Solving,

$x=\frac{R}{2}$

$\therefore$ Option C is correct.