We know that electric field is discontinuous across the surface of a charged conductor. Is electric potential also discontinuous there?

Explanation

To determine whether electric potential is discontinuous across the surface of a charged conductor, we can follow these steps:

### Step 1: Understanding Electric Field and Electric Potential
The electric field (E) and electric potential (V) are related concepts in electrostatics. The electric field is defined as the force per unit charge experienced by a small positive test charge placed in the field, while the electric potential is the work done to bring a unit positive charge from infinity to a point in the field.

### Step 2: Electric Field Discontinuity on a Charged Conductor
For a charged conductor, the electric field is indeed discontinuous at the surface. Inside the conductor, the electric field is zero (E = 0), while just outside the surface, it has a finite value. This discontinuity arises because the charges reside on the surface of the conductor, creating a strong electric field just outside.

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