Electrostatics> two spherical conductors of radii 4m and ...

two spherical conductors of radii 4m and 5m are charged tto same potential. ti sigma and sigma2 be the respective values of surface density of charge on two conductors then thr ratio of sigma1 is to sigma2 is
A.25/16 B.16/25
C.5/4 D.4/5

TIlak , 7 Years ago

Grade 12

2 Answers

Eshan

Last Activity: 7 Years ago

Potential of a spherical conductor of radius $r$ carrying a charge $Q$ = $\dfrac{kQ}{r}$ .

Since the two spherical conductors are charged to same potential,

$\dfrac{kQ_1}{r_1}=\dfrac{kQ_2}{r_2}$
$\implies \dfrac{Q_1}{Q_2}=\dfrac{r_1}{r_2}$
Hence the ratio of surface charge densities= $\dfrac{\sigma_1}{\sigma_2}=\dfrac{Q_1/(4\pi r_1^2)}{Q_2/(4\pi r_2^2)}$
$=\dfrac{r_2}{r_1}$
$=\dfrac{5}{4}$

Gitanjali Rout

Last Activity: 7 Years ago

$=\dfrac{r_2}{r_1}$ $\dfrac{\sigma_1}{\sigma_2}=\dfrac{Q_1/(4\pi r_1^2)}{Q_2/(4\pi r_2^2)}$ Hence the ratio of surface charge densities= $\implies \dfrac{Q_1}{Q_2}=\dfrac{r_1}{r_2}$ $\dfrac{kQ_1}{r_1}=\dfrac{kQ_2}{r_2}$ Since the two spherical conductors are charged to same potential,