Question

The conducting spheres of radius r and 2r at very large separation. Each sphere is having charge Q. These spheres are connected with a conducting wire of resistance R. Then, the current flowing in the wire at $t=2\mu s$. (Where r = 30cm, $R=90k\Omega$ and $Q=10\mu C)$)

• A. $\frac{100}{3e}amp$
• B. $\frac{5}{3e}amp$
• C. $\frac{50}{3e}amp$
• D. $\frac{25}{3e}amp$

Answer 1

The correct option is B $\frac{5}{3e}amp$

$\frac{K(2Q-q)}{r}-\frac{kq}{2r}=\frac{dq}{dt}R$
$\int \frac{K}{rR}dt=\int \frac{dq}{2Q-\frac{3q}{2}}$
$4Q-3q=Q{e}^{-\frac{3kt}{2rR}}$

Differentiating w.r.t time
$-\frac{3dq}{dt}=-\frac{3}{2}\frac{KQ}{rR}{e}^{-\frac{3kt}{2rR}}$
$i=\frac{1}{8\pi {ϵ}_{0}rR}{e}^{-\frac{3t}{8\pi {ϵ}_{0}rR}}$