The surface of a conductor -

Options

A. is a non-equipotential surface
B. has all the points at the same potential
C. has different points at different potential
D. has at least two points at the same potential

Answer

To solve the question regarding the surface of a conductor, we need to understand the properties of conductors in electrostatics. Here’s a step-by-step breakdown of the solution:

### Step 1: Understanding Conductors in Electrostatics
When a conductor is placed in an external electric field, free charges (electrons) within the conductor move in response to that field. This movement leads to polarization, where one side of the conductor becomes negatively charged and the opposite side becomes positively charged.

**Hint:** Remember that conductors have free charges that can move easily in response to electric fields.

### Step 2: Electric Field Inside the Conductor
In electrostatic equilibrium, the electric field inside a conductor is zero. This is because the induced electric field created by the movement of charges cancels the external electric field. Thus, the net electric field inside the conductor is zero.

**Hint:** Think about Gauss's law and how it applies to the electric field within conductors.

### Step 3: Implication of Zero Electric Field
Since the electric field inside the conductor is zero, the potential (V) must be constant throughout the conductor. The electric field is related to the potential by the equation \( E = -\frac{dV}{dr} \). If \( E = 0 \), then \( \frac{dV}{dr} = 0 \), which implies that the potential does not change.

**Hint:** Recall that if the electric field is zero, the potential must be uniform.

### Step 4: Conclusion about the Surface of the Conductor
Because the potential is constant throughout the conductor, all points on the surface of the conductor must also be at the same potential. Therefore, the correct statement regarding the surface of a conductor is that it has all points at the same potential.

**Hint:** Remember that the surface of a conductor is always an equipotential surface in electrostatics.

### Final Answer
The correct option is: **The surface of a conductor has all the points at the same potential.**