Question

A point charge of magnitude $+1\mu c$ is fixed at $(0,0,0)$. An isolated uncharged spherical conductor is fixed its centre at $(4m,0,0)$. The potential and the induced electric field at the centre of the sphere is

• A. $1.8\times {10}^{5}V$ and $-5.625\times {10}^{6}V/m$
• B. $0Vand0V/m$
• C. $2.25\times {10}^{5}V$ and $-5.625\times {10}^{6}V/m$
• D. $2.25\times {10}^{5}V$ and $0V/m$

Answer 1

The correct option is C $2.25\times {10}^{5}V$ and $-5.625\times {10}^{6}V/m$

Given,

$q=1\mu C=1\times {10}^{-16}C$

$r=4cm=4\times {10}^{-2}m$

Potential, $V=\frac{kq}{r}$

$=\frac{9\times {10}^9\times {10}^{-6}}{4\times {10}^{-2}}=2.25\times {10}^{5}V$

Induced electric fiels, $E=\frac{kq}{r^2}$

$=\frac{9\times {10}^9\times 1\times {10}^{-6}}{16\times {10}^{-4}}=-5.625\times {10}^{6}V/m$