Question 420: Electrostatics & Capacitance

Question

Concentric metallic hollow spheres of radii R and 4R hold charges Q
1
and Q
2
respectively. Given that
surface charge densities of the concentric spheres are equal, the potential difference V(R) – V(4R) is :

Accepted Answer

$$\sigma  = {{{Q_1}} \over {4\pi {R^2}}} = {{{Q_2}} \over {4\pi 16{R^2}}}$$
$$ \Rightarrow $$ $$16{Q_1} = {Q_2}$$
$$ 	herefore $$ $${V_R} - {V_{4R}} = {{K{Q_1}} \over R} + {{K{Q_2}} \over {4R}} - {{K{Q_1}} \over {4R}} - {{K{Q_2}} \over {4R}}$$
$$ = {{3K{Q_1}} \over {4R}} = {{3{Q_1}} \over {16\pi {\varepsilon _0}R}}$$ [As K = $${1 \over {4\pi {\varepsilon _0}}}$$ ]

Answer

$${{3{Q_2}} \over {4\pi {\varepsilon _0}R}}$$

Answer

$${{3{Q_1}} \over {4\pi {\varepsilon _0}R}}$$

Answer

$${{3{Q_1}} \over {16\pi {\varepsilon _0}R}}$$

Answer

$${{{Q_2}} \over {4\pi {\varepsilon _0}R}}$$

Electrostatics & Capacitance

Concentric metallic hollow spheres of radii R and 4R hold charges Q 1 and Q 2 respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference V(R) – V(4R) is :

Choose the correct answer: