Explain the variations of potential and field intensity with distance due to a hollow charged spherical conductor (radius a and charge q), both inside and outside the sphere, with a graph.

Explanation

Electric potential : Potential at all points inside a hollow charged spherical conductor and on its surface are equal. Here this potential is , `V = q/a`. So, from the centre to the surface of the conductor, potential is constant and it has been shown be the line AB, parallel to x-axis.
If the distance of an external point from the centre of the conductor be r, then electric potential at that point is given by, `V = q/r`. So as r increases, V decreases. This decrease has been shown by the curved line BC. The inverse variation is illustrated by the moderate slope of the curve.
Electric intensity: As the potential at all points inside a hollow charged spherical conductor is a constant, intensity at those points, i.e., inside the hollow spherical conductor is zero. As the radius of the conductor is a, intensity at a point on its surface, `E = q/(a^2)`. If r be the distance of an external point from the centre of the sphere, intensity at that point will be `E = q/(r^2)`.

So, intensity on the surface of the conductor is maximum and it decreases as we move away from the conductor. This variation has shown by the curved line AB. The inverse square variation has been shown by the steeper slope, as compared to the V-r curve.