The electrostatic potential of a uniformly charged thin spherical shell of charge Q and radius R at a distance `r` from the centre

Options

A. `(Q)/(4 pi epsilon_(0)r)` for points outside and `(Q)/(4pi epsilon_(0)R)` for points inside the shell
B. `(Q)/(4pi epsilon_(0)e)` for both points inside nad outside the shell
C. zero for points outside and `(Q)/(4pi epsilon_(0)r)` for points inside the shell
D. zero for both points inside and outside the shell

Answer

To find the electrostatic potential \( V \) of a uniformly charged thin spherical shell of charge \( Q \) and radius \( R \) at a distance \( r \) from the center, we need to consider two cases: when the point of interest is inside the shell (i.e., \( r < R \)) and when it is outside the shell (i.e., \( r \geq R \)).

### Step 1: Determine the potential inside the shell (when \( r < R \))

For a uniformly charged thin spherical shell, the electric field inside the shell is zero. Therefore, the potential \( V \) inside the shell is constant and equal to the potential at the surface of the shell.

The potential at the surface of the shell can be calculated using the formula:
\[ V = \frac{KQ}{R} \]
where \( K = \frac{1}{4\pi \epsilon_0} \).

Thus, for \( r < R \):
\[ V_{\text{inside}} = \frac{KQ}{R} \]

### Step 2: Determine the potential outside the shell (when \( r \geq R \))

For points outside the shell, the shell can be treated as a point charge located at its center. The potential at a distance \( r \) from the center is given by:
\[ V = \frac{KQ}{r} \]

Thus, for \( r \geq R \):
\[ V_{\text{outside}} = \frac{KQ}{r} \]

### Conclusion

In summary, the electrostatic potential \( V \) of a uniformly charged thin spherical shell is given by:
- For \( r < R \):
\[ V = \frac{KQ}{R} \]
- For \( r \geq R \):
\[ V = \frac{KQ}{r} \]