Assertion : Five charges `+q` each are placed at five vertices of a regular pentagon. A sixth xharge `-Q` is placed at the centre of pentagon. Then, net electrostatic force on `-Q` is zero.
Reason : Net electrostatic potential at the centre is zero.

Options

A. If both Assertion and Reason are true and Reason is the correct explanation of Assertion.
B. If both Assertion and Reason are true but Reason is not correct explanation of Assertion.
C. If Assertion is true but Reason is false.
D. If Assertion is false but Reason is true.

Answer

To solve the question, we need to analyze the assertion and reason provided:

### Assertion:
Five charges `+q` each are placed at five vertices of a regular pentagon. A sixth charge `-Q` is placed at the center of the pentagon. Then, the net electrostatic force on `-Q` is zero.

### Reason:
Net electrostatic potential at the center is zero.

### Step-by-Step Solution:

1. **Understanding the Configuration**:
- We have five positive charges `+q` located at the vertices of a regular pentagon.
- A negative charge `-Q` is placed at the center of the pentagon.

2. **Analyzing the Forces on Charge `-Q`**:
- Each positive charge `+q` exerts an attractive force on the negative charge `-Q`.
- Due to the symmetry of the pentagon, the forces exerted by the five charges on `-Q` will be equal in magnitude but will act in different directions.

3. **Symmetry and Resultant Force**:
- The five forces will be symmetrically distributed around the center.
- Since the angles between the lines connecting the center to each vertex are equal (72 degrees), the resultant force on the charge `-Q` will be zero.
- Thus, the assertion is true: the net electrostatic force on `-Q` is zero.

4. **Calculating the Electrostatic Potential**:
- The electrostatic potential `V` at a point due to a point charge is given by the formula:
\[ V = k \frac{q}{r} \]
where `k` is Coulomb's constant, `q` is the charge, and `r` is the distance from the charge to the point of interest.
- For the charge `-Q` at the center, the potential due to each `+q` charge is the same, and since there are five such charges, the total potential at the center is:
\[ V_{\text{total}} = 5 \cdot k \frac{q}{r} \]
- This potential is non-zero because it is a scalar quantity and adds up.

5. **Conclusion**:
- The assertion is true, but the reason is false. The net electrostatic potential at the center is not zero; it is a non-zero value due to the presence of the five positive charges.

### Final Answer:
- Assertion: True
- Reason: False