Animated Solution for Physics - Electrostatics: A metallic shell has a point charge $q$ kept inside its cavity. Which one of the following diagrams correctly represents the electric lines of forces ?

Imagine a thick, solid metallic shell. Deep inside this shell lies a spherical cavity, and within this cavity, we place a point charge $q$.

But here is the twist: the charge is not placed at the center of the cavity. It is shifted to one side.

Our mission is to map the electric field lines for this entire system. To do this, we must rely on the fundamental laws of electrostatics governing conductors.

Before we draw a single line, we must establish the ground rules.

First, the electric field inside the solid material of a conductor in electrostatic equilibrium is always exactly zero ($E=0$). If it weren't, the free electrons inside the metal would move, which contradicts the state of equilibrium. Therefore, no electric field lines can exist inside the solid metallic region.

Second, the surface of a conductor is an equipotential surface. This means that any electric field line touching the surface must intersect it at exactly $90^{\circ }$. If the lines hit at an angle, there would be a tangential component of the electric field, causing charges to flow along the surface.

A Curved Reality

Let's apply these rules to the inside of the cavity. The electric field lines must originate from the positive charge $q$ and travel outwards to hit the inner surface of the cavity.

Because the surface is an equipotential, the lines must strike it perpendicularly. For a spherical surface, a perpendicular line must align with the radius of the sphere.

If the charge $q$ were at the center, the lines would simply be straight radial lines. However, because $q$ is off-center, straight lines originating from it will hit the surface at an angle. To satisfy the $90^{\circ }$ rule, the field lines must curve as they travel from the charge to the inner surface.

The Great Illusion

Now, let's look at the outside of the shell. The positive charge $q$ inside the cavity attracts negative charges, inducing a charge of $-q$ on the inner surface. This leaves a net charge of $+q$ on the outer surface.

Here is where the magic of electrostatic shielding happens. The solid metal completely isolates the outside world from the inside. The outer surface only "knows" that it has a total charge of $+q$ to distribute.

Because the outer surface is a perfect sphere, this positive charge will distribute itself perfectly uniformly. It has absolutely no memory of the fact that the original charge $q$ is sitting off-center inside the cavity.

Because the charge distribution on the outer surface is uniform, the electric field it creates outside the shell is perfectly symmetric.

The field lines will emerge radially from the geometric center of the outer sphere, and they will be uniformly spaced.

Comparing our logical deductions with the given options, only diagram (c) captures the full physical reality: curved lines inside the cavity to meet the inner surface orthogonally, and straight, uniform, radial lines outside the shell.