Question

The electric potential inside a conductor:
A) is zero
B) increases with distance from the centre
C) is constant
D) decreases with distance from the centre

Answer 1

Hint: The electrostatic field inside a conductor is zero as the charges only reside on the surface of the conductor. Since the electrostatic field is defined as the negative gradient of the electrostatic potential, we can easily determine the potential on the inside of the conductor.

Formula used:
-The electrostatic field is given by, $E=-{\displaystyle \frac{dV}{dr}}$ where $V$ is the electrostatic potential and $r$ is the distance from the charge.

Complete step by step solution:
Step 1: Based on the value of the electric field $E$ obtain the electric potential $V$ inside the conductor.
A conductor has free charges. But the charges will distribute themselves such that no charge is present on the inside of the conductor. Since an electric field requires the presence of a charge, the electric field inside the conductor will be zero i.e., $E=0$ .

Now the electrostatic field can be expressed as $E=-{\displaystyle \frac{dV}{dr}}$ .

Inside the conductor we have $E=-{\displaystyle \frac{dV}{dr}}=0$

$\Rightarrow V=\text{constant}$

Thus the electric potential will be constant inside the conductor.

So the correct option is C.

Additional information:An application of the zero electric field inside a conductor is electrostatic shielding. It is often mentioned that during lightning, it is safer to be in a car. This is because the car which is a conductor will have no charges on its inside and hence even if it gets struck by lightning, the charges will reside only on the outer surface of the car.

Note: A zero electric field inside the conductor indicates that no potential difference exists between two points on the inside of the conductor. Since zero is also a constant number, the electrostatic potential inside the conductor can also be taken to be zero. So option A can also be considered as the correct option. However, the potential inside the conductor must match the potential on the surface of the conductor.