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 $q^{\prime }$ be the charges on spheres of radii $R$ and $2R$ respectively.
Given $q+q^{\prime }=Q$ ... (1)
Surface charge densities are
$\sigma =\frac{q}{4\pi R^2}\sigma =\frac{q^{\prime }}{4\pi (2R{)}^2}$
Given $\sigma ={\sigma }^{\prime }$
$\therefore \frac{q}{4\pi R^2}=\frac{q^{\prime }}{4\pi (2R{)}^2}$
or $q^{\prime }=4q$
From eq (1) $q^{\prime }=Q-q4q=Q-qQ=5q$ ...(2)
$q^{\prime }=Q-q=Q-\frac{Q}{5}=\frac{4Q}{5}$