Two small spheres, each carrying a charge q are placed r m apart and they interact with force F. If one of the sphere is taken around the other once in a circular path, the work done will be equal to

Options

A. 0
B. F
C. 2F
D. `F//2`

Explanation

To solve the problem, we need to determine the work done when one sphere is taken around the other in a circular path. Let's break down the solution step by step.

### Step 1: Understand the System
We have two small spheres, each carrying a charge \( q \), separated by a distance \( r \). They exert a force \( F \) on each other due to their charges.

**Hint:** Remember that the force between two charges is given by Coulomb's law.

### Step 2: Identify the Nature of the Path
One of the spheres is moved in a circular path around the other sphere. As the sphere moves, we need to consider the nature of the electric field created by the other sphere.

**Hint:** Consider how the electric field behaves around a charged sphere.

### Step 3: Electric Field and Equipotential Surfaces
The electric field created by a point charge (or a charged sphere) radiates outward in all directions. The equipotential surfaces around a point charge are spherical surfaces where the potential is constant.

**Hint:** Recall that on an equipotential surface, the electric potential does not change.

### Step 4: Work Done in Moving a Charge
The work done \( W \) in moving a charge \( q \) in an electric field is given by the equation:
\[ W = q \cdot V \]
where \( V \) is the potential difference. However, if the charge is moved along an equipotential surface, the potential difference is zero.

**Hint:** Think about what happens when you move a charge along a path where the potential is constant.

### Step 5: Conclusion on Work Done
Since the sphere is moved in a circular path around the other sphere, it is effectively moving along an equipotential surface. Therefore, the work done in this case is:
\[ W = 0 \]

### Final Answer
The work done when one sphere is taken around the other once in a circular path is equal to **zero**.