Question

A thin spherical conducting shell of radius $R$ has a charge q. Another charge $Q$ is placed at the center of the shell. The electric potential at a point $P$ at distance $\frac{R}{2}$ from the center of the shell is $( Q =10 \mu C , q =-2 \mu C )$

• A. $\frac{1.6 \times 10^{5}}{ R }$ volt
• B. $1.6 \times 10^{5} R$ volt
• C. $\frac{1.4 \times 10^{5}}{ R }$ volt
• D. $\frac{4 \times 10^{-6}}{ R }$ volt

Answer 1

Answer: (C)

Electric potential at point $P$
$V _{ P }=\frac{ KQ }{ r }+\frac{ K q }{ r }$
$V_{P}=\frac{K Q}{\frac{R}{2}}-\frac{K q}{\frac{R}{2}}$
$V_{P}=\frac{2 K}{R}(10-2) 10^{-6}$
$=\frac{2 \times 9 \times 10^{9} \times 8 \times 10^{-6}}{ R }=\frac{144 \times 10^{3}}{ R }$ volt
$V _{ P }=\frac{1.44 \times 10^{5} volt }{ R }$