Question

Charge $Q$ is distributed to two different metallic spheres having radii $R$ and $2R$ such that both spheres have equal surface charge density, then charge on large sphere is :

• A. $\frac{4Q}{5}$
• B. $\frac{Q}{5}$
• C. $\frac{3Q}{5}$
• D. $\frac{5Q}{4}$

Answer 1

Answer: (A)

$\frac{4Q}{5}$

Let $q$ and $q^{\prime }$ be the charges on spheres of radii $R$ and $2R$ respectively.
Given $q+q^{\prime }=Q.......\left(1\right)$
Surface charge densities are
$\sigma =\frac{q}{4\pi R^2}\sigma =\frac{q^{\prime }}{4\pi {\left(2R^{}\right)}^2}$
Given $\sigma ={\sigma }^{\prime }$
$\therefore \frac{q}{4\pi R^2}=\frac{q^{\prime }}{4\pi {\left(2R^{}\right)}^2}or{q}^{\prime }=4q$

From eq $\left(1\right)$ $q^{\prime }=Q-q4q=Q-qQ=5q.......\left(2\right)$
$q^{\prime }=Q-q=Q-\frac{Q}{5}=\frac{4Q}{5}$