Question

The electric potential on the surface of a charged spherical conductor of radius $5cm$ is $200V$. Work done in moving a charge of $+5C$ from a point $A$ to another point $B$ situated at distances of $15cm$ and $10cm$ respectively from the centre of the sphere is_________

• A. 16.7 J
• B. 23.3 J
• C. 88.8 J
• D. 166.7 J

Answer 1

Answer: (D)

Electric potential on the surface of sphere, $V=200V$ Radius, $R=5cm=5\times 10^{-2}m$
Charge, $q=5C$

Electric potential on the surface of sphere,
$V=9\times 10^9\frac{Q}{R}$
$200=9\times 10^9\cdot \frac{Q}{5\times 10^{-2}}$
$\Rightarrow Q=\frac{10^{-8}}{9}C$
Work done to move the charge from point $A$ to point $B$ is given as
$W=V_{AB}\cdot q$
$=\left(V_B-V_A\right)q=\left(9\times 10^9\cdot \frac{Q}{r_B}-9\times 10^9\cdot \frac{Q}{r_A}\right)5$
$=9\times 10^9\left(\frac{10^{-8}}{9\times 10^{-1}}-\frac{10^{-8}}{9\times 15\times 10^{-2}}\right)5$
$=45\times 10^9\times 10^{-8}\left[\frac{1}{9\times 10^{-1}}-\frac{1}{9\times 15\times 10^{-2}}\right]$
$=450\times \frac{1}{9}\left[10-\frac{100}{15}\right]=50\left[\frac{50}{15}\right]$
$=166.66J=166.7J$