Question

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

• A. $1.8\times10^{5}\,V$ and $-5.625 \times 10^{6}\, V/m$
• B. $0\,V$ and $0\,V/m$
• C. $2.25\times10^{5}\,V$ and $-5.625 \times 10^{6}\, V/m$
• D. $2.25\times10^{5}\,V$ and $0\, V/m$

Answer 1

Answer: (C)

$q=1\,\mu C=1\times10^{-6}C$
$r=4\,cm = 4\times10^{-2}\,m$
Potential $V=\frac{kq}{r}$
$=\frac{9\times10^{9}\times10^{-6}}{4\times10^{-2}}$
$=2.25\times10^{5}V$.
Induced electric field $E=-\frac{kq}{r^{2}}$
$=\frac{9\times10^{9}\times1\times10^{-6}}{16\times10^{-4}}=-5.625\times10^{6}\,V/m$