Q. A conducting sphere of radius $10cm$ is charged $10\mu\ C.$ Another uncharged sphere of radius $20\ cm$ is allowed to touch it for some time. After that if the sphere are separated, then surface density of charges, on the spheres will be in the ratio of
A) 1 : 4
B) 1 : 3
C) 2 : 1
D) 1 : 1
Explanation
(c) After redistribution new charges on spheres are
$Q_{1}^{'} = \left( \frac{10}{10 + 20} \right) \times 10 = \frac{10}{3}\mu C$
And $Q_{2}^{'} = \left( \frac{20}{10 + 20} \right) \times 10 = \frac{20}{3}\mu C$
Ratio of charge densities $\frac{\sigma_{1}}{\sigma_{2}} = \frac{Q_{1}^{'}}{Q_{2}^{'}} \times \frac{r_{2}^{2}}{r_{1}^{2}}$
$= \frac{10/3}{20/3} \times \left( \frac{20}{10} \right)^{2} = \frac{2}{1}\ \ \ \ \ \left\lbrack \sigma = \frac{Q}{4\pi r^{2}} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.