For a uniformly charged thin spherical shell, the electric potential $$V$$ radially away from the centre $$O$$ of shell can be graphically represented as

(1)

(2)

(3)

(4)

For a uniformly charged thin spherical shell of radius R, electric potential varies with distance r from the centre as follows:

For r≤R (inside and on the shell)

Electric field inside a conducting shell is zero:

E=0

Since

$$E=-\frac{dV}{dr}$$

zero electric field means potential is constant throughout the interior.

Its value equals the surface potential:

$$V=\frac{1}{4\pi\varepsilon_0}\frac{Q}{R}$$

So for all

0≤r≤R

potential remains constant and maximum.

For r>R (outside the shell)

The shell behaves like a point charge concentrated at the centre:

$$V=\frac{1}{4\pi\varepsilon_0}\frac{Q}{r}$$

Thus

$$V\propto\frac{1}{r}$$

and decreases with distance.

Graphical variation:

• From r=0 to r=R: horizontal straight line (constant potential)
• At r=R: potential is continuous,

$$V=\frac{Q}{4\pi\varepsilon_0R}$$

• For r>R: a decreasing $$\frac{1}{r}$$ curve approaching zero as

$$r\longrightarrow \infty$$

So the graph is a flat line inside the shell followed by a falling hyperbolic curve outside.