Relationship between VA, VB, and Vc on the surface of a hollow conducting sphere in an electric field

Introduction:
When a hollow conducting sphere is placed in an electric field produced by a point charge, the potential at different points on the surface of the sphere will vary. The potential at point A (VA), point B (VB), and point C (Vc) on the surface of the sphere can be related to each other based on the properties of a conducting sphere and the electric field produced by the point charge.

Understanding the properties of a conducting sphere:
1. Electric field inside a conductor is zero: In a conducting material, charges are free to move, and they redistribute themselves in such a way that the electric field inside the conductor becomes zero. Therefore, the electric field inside the hollow conducting sphere is zero.

2. Electric field is perpendicular to the surface: At every point on the surface of a conductor, the electric field is perpendicular to the surface. This is because any component of the electric field parallel to the surface would cause charges to move along the surface until the field becomes perpendicular.

3. The potential is constant on the surface: Since the electric field is perpendicular to the surface of the conducting sphere, the potential is constant at every point on the surface. Therefore, VA, VB, and Vc will have the same value.

Explanation of the relationship between VA, VB, and Vc:
- Since the electric field inside the hollow conducting sphere is zero, the potential at all points inside the sphere is constant and equal to the potential at the surface.
- As mentioned earlier, VA, VB, and Vc are all on the surface of the sphere, so they will have the same potential.
- Therefore, the relationship between VA, VB, and Vc is that they are all equal.

Summary:
When a hollow conducting sphere is placed in an electric field produced by a point charge, the potential at different points on the surface of the sphere will be the same. This is because the electric field inside the conductor is zero, and the potential is constant on the surface. Therefore, VA, VB, and Vc will all have the same value.