Physics

Problem

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: a.

\frac{3Q_1}{16\pi\epsilon_0 R}

\frac{3Q_2}{4\pi\epsilon_0 R}

\frac{Q_2}{4\pi\epsilon_0 R}

\frac{3Q_1}{4\pi\epsilon_0 R}

Intuitive explanation

The key insight is that equal surface charge densities on spheres of different radii means the total charges are proportional to their surface areas. Since surface area scales as $r^2$ , you can find the relationship between $Q_1$ and $Q_2$ , then use the fact that potential difference depends on how charge is distributed in the spheres. The potential at each radius comes from all the charge enclosed and the charge on the outer sphere, so set up the potential using Coulomb's law for spherical symmetry.

Intuitive explanation

Browse the problem library