Q9CQ - College Physics (Urone)

Question

In what region of space is the potential due to a uniformly charged sphere the same as that of a point charge? In what region does it differ from that of a point charge?

Step-by-Step Solution

Answer

Both electric potential are similar for regions outside the sphere and differ within the sphere.

Step 1: Definition of electric potential

At any distance r from the charge, the electric potential V owing to a point charge q is-

 $\mathbf{V}\mathbf{=}\mathbf{k}\frac{\mathbf{q}}{\mathbf{r}}$

where k is a coulomb's constant.

Step 2: Final result and explanation

At distances r outside the sphere, the electric potential of a uniformly charged sphere is similar to that of a point charge; that is, for r > R  ,where R is the radius of the sphere.

Inside the charged sphere, the electric potential is zero; that is for 0 < r < R .

This is the point at which the charged sphere's electric potential differs from that of a point charge.