Electrostatics Question 122
Question: 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 [AIIMS 2002]
Options:
A) 1 : 4
B) 1 : 3
C) 2 : 1
D) 1 : 1
Show Answer
Answer:
Correct Answer: C
Solution:
After redistribution new charges on spheres are
$ Q{’ _{1}}=( \frac{10}{10+20} )\times 10=\frac{10}{3}\mu C $ and $ Q{’ _{2}}=( \frac{20}{10+20} )\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 {{( \frac{20}{10} )}^{2}}=\frac{2}{1} $
$ { \sigma =\frac{Q}{4\pi r^{2}} } $
