Question

A sphere of $10\, cm$ diameter is suspended within a hollow sphere of $12\, cm$ diameter. If the inner sphere be charged to a potential of $15,000 \,V$ 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 $r_{1}=0.05\, m , r_{2}=0.06\, m$
$C=\frac{4 \pi \varepsilon_{0} r_{1} r_{2}}{\left(r_{2}-r_{1}\right)}=\frac{0.05 \times 0.06}{0.01\left(9 \times 10^{9}\right)}=\frac{1}{3} \times 10^{-10} F$
Potential difference between the plates, $V=15,000 \,V$
$\therefore $ Charge on the inner sphere,
$C V=\frac{1}{3} \times 10^{-10} \times 15,000=5 \times 10^{-7} C$