Question

A sphere of $10cm$ diameter is suspended within a hollow sphere of $12cm$ diameter. If the inner sphere be charged to a potential of $15,000V$ and the outer sphere be earthed, the charge on the inner sphere is

• A. $5\times 10^{-7}C$
• B. $6\times 10^{-7}C$
• C. $7\times 10^{-7}C$
• D. $8\times 10^{-7}C$

Answer 1

Answer: (A)

Here $r_1=0.05m,r_2=0.06m$
$C=\frac{4\pi {\epsilon }_0{r}_1{r}_2}{\left(r_2-r_1\right)}=\frac{0.05\times 0.06}{0.01\left(9\times 10^9\right)}=\frac{1}{3}\times 10^{-10}F$
Potential difference between the plates, $V=15,000V$
$\therefore$ Charge on the inner sphere,
$CV=\frac{1}{3}\times 10^{-10}\times 15,000=5\times 10^{-7}C$