Nature of equipotential surface for a point charge is

Options

A. ellopsoid with charge at foci
B. sphere with charge at the centre of the sphere
C. sphere with charge on the surface of the sphere
D. plane with charge on the surface

Answer

To determine the nature of the equipotential surface for a point charge, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Equipotential Surfaces**:
- An equipotential surface is defined as a surface where the electric potential is constant. This means that if you move along this surface, the potential does not change.

2. **Electric Field of a Point Charge**:
- The electric field \( E \) due to a point charge \( Q \) at a distance \( r \) from the charge is given by the formula:
\[ E = \frac{kQ}{r^2} \]
where \( k \) is Coulomb's constant.

3. **Direction of Electric Field**:
- The electric field due to a point charge radiates outward (for a positive charge) or inward (for a negative charge). This means that at any point in space, the electric field vector points away from the charge (for positive charge) and is directed towards the charge (for negative charge).

4. **Shape of Equipotential Surfaces**:
- Since the electric field is radial and the potential is constant at every point on the equipotential surface, the equipotential surfaces around a point charge are spherical. This is because the distance from the point charge remains constant on a sphere.

5. **Conclusion**:
- Therefore, the nature of the equipotential surface for a point charge is spherical. Each spherical surface at a different radius from the charge represents a different equipotential surface, but all points on a given sphere have the same electric potential.

### Final Answer:
The nature of the equipotential surface for a point charge is spherical.

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