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. $\frac{5Q}{5}$

Answer 1

Answer: (A)

Let $q$ and $q'$ be the charges on spheres of radii $R$ and $2 R$ respectively.
Given $q+q'=Q$ ... (1)
Surface charge densities are
$\sigma=\frac{q}{4 \pi R^{2}}\,\,\sigma=\frac{q'}{4 \pi(2 R)^{2}}$
Given $\sigma=\sigma'$
$\therefore \frac{q}{4 \pi R^{2}}=\frac{q'}{4 \pi(2 R)^{2}}$
or $q'=4 q$
From eq (1) $q'=Q-q\,\,4 q=Q-q\,\,Q=5 q$ ...(2)
$q'=Q-q=Q-\frac{Q}{5}=\frac{4 Q}{5}$