Question

The electric potential on the surface of a charged spherical conductor of radius $5\, cm$ is $200\, V$. Work done in moving a charge of $+5 C$ from a point $A$ to another point $B$ situated at distances of $15\, cm$ and $10\, cm$ 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, $V=200\, V$ Radius, $R=5\, cm =5 \times 10^{-2} m$
Charge, $q=5\, C$

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
$W=V_{A B} \cdot q$
$=\left(V_{B}-V_{A}\right) q=\left(9 \times 10^{9} \cdot \frac{Q}{r_{B}}-9 \times 10^{9} \cdot \frac{Q}{r_{A}}\right) 5$
$=9 \times 10^{9}\left(\frac{10^{-8}}{9 \times 10^{-1}}-\frac{10^{-8}}{9 \times 15 \times 10^{-2}}\right) 5$
$=45 \times 10^{9} \times 10^{-8}\left[\frac{1}{9 \times 10^{-1}}-\frac{1}{9 \times 15 \times 10^{-2}}\right]$
$=450 \times \frac{1}{9}\left[10-\frac{100}{15}\right]=50\left[\frac{50}{15}\right]$
$=166.66\, J =166.7\, J$