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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

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

Grade:12

2 Answers

Eshan
askIITians Faculty 2095 Points
4 years ago
Potential of a spherical conductor of radiusrcarrying a chargeQ=\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
184 Points
4 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,

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