In the following question a statement of assertion (A) is followed by a statement of reason (R )
A : One may have zero potential but non-zero electric field at a point in space.
R : Potential is a scalar quantity .

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion , then mark (1).
B. If both Assertion & Reason are true but the reason is not correct explanation of the assertion then mark (2)
C. If Assertion is true statement but Reason is false, then mark (3)
D. If both Assertion and Reason are false statements , then mark (4).

Answer

To solve the question, we need to analyze the assertion (A) and the reason (R) provided.

**Assertion (A)**: One may have zero potential but non-zero electric field at a point in space.

**Reason (R)**: Potential is a scalar quantity.

### Step-by-Step Solution:

1. **Understanding Electric Potential**:
- Electric potential (V) at a point in space is defined as the work done per unit charge in bringing a positive test charge from infinity to that point without any acceleration.
- The formula for electric potential due to a point charge \( Q \) at a distance \( r \) is given by:
\[ V = \frac{kQ}{r} \]
where \( k \) is Coulomb's constant.

2. **Understanding Electric Field**:
- The electric field (E) at a point in space is defined as the force per unit charge experienced by a positive test charge placed at that point.
- The electric field due to a point charge \( Q \) is given by:
\[ E = \frac{kQ}{r^2} \]

3. **Analyzing the Assertion**:
- The assertion states that it is possible to have zero potential (V = 0) but a non-zero electric field (E ≠ 0).
- Consider a system with two point charges: a positive charge (+Q) and a negative charge (-Q) placed symmetrically about a point P. At point P, the potentials due to both charges can cancel each other out, resulting in \( V = 0 \).
- However, the electric field at point P is not zero because the electric fields due to the two charges do not cancel out; they will still produce a net electric field pointing towards the negative charge.

4. **Analyzing the Reason**:
- The reason states that potential is a scalar quantity. This is true because electric potential does not have a direction; it only has magnitude.
- The scalar nature of potential allows for the algebraic addition of potentials from multiple charges, which can lead to a situation where the total potential is zero.

5. **Conclusion**:
- Both the assertion and the reason are correct. The assertion correctly describes a scenario where the potential is zero while the electric field is non-zero, and the reason correctly identifies the scalar nature of electric potential as the underlying cause for this phenomenon.

### Final Answer:
Both the assertion (A) and the reason (R) are correct.

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