Question

A conducting sphere of radius $10$ $cm$ is charged with $10$ $\mu C$. Another uncharged sphere of radius $20$ $cm$ is allowed to touch it for some time. After that if the spheres are separated, then surface density of charges on the spheres will be in the ratio of

• A. $1:1$
• B. $4:1$
• C. $1:3$
• D. $1:4$

Answer 1

The correct option is B $4:1$

Potential will be same on both the spheres.

$Are{a}_1\cdot {\rho }_{s1}=Are{a}_2\cdot {\rho }_{s2}$

$\Rightarrow 4\pi r_1^2\cdot {\rho }_{s1}=4\pi r_2^2\cdot {\rho }_{s2}$

$\Rightarrow \frac{{\rho }_{s1}}{{\rho }_{s2}}=\frac{r_2^2}{r_1^2}$

$\Rightarrow \frac{{\rho }_{s1}}{{\rho }_{s2}}=\frac{{20}^2}{{10}^2}=\frac{4}{1}$

$\Rightarrow 4:1$