Question

Assertion (A): In a region of constant potential, the electric field is zero and there can be no charge inside the region.
Reason (R): According to Gauss law, charge inside the region should be zero if electric field is zero.

• A. Both (A) and (R) are true; (R) is correct explanation of (A)
• B. Both (A) and (R) are true; (R) is not correct explanation of (A)
• C. (A) is true, (R) is false
• D. (A) is false, (R) is true

Hint:

A constant electric potential implies zero electric field because \[ \vec{E}=-\nabla V \] Gauss law relates electric flux to enclosed charge.

Answer 1

The Correct Option is B

Step 1: Examine the assertion carefully.
The assertion claims that in a region of constant potential the field is zero and there can be no charge inside that region.
Step 2: Confirm the field part of the assertion.
Since $\vec{E} = -\nabla V$, a potential that is constant everywhere in the region gives $\nabla V = 0$, hence \[ \vec{E} = 0 \] So the field-is-zero part is correct.
Step 3: Test the no-charge claim with Gauss law.
Gauss law states $\displaystyle\oint \vec{E}\cdot d\vec{A} = \dfrac{q_{\text{enc}}}{\varepsilon_0}$. If $\vec{E}=0$ over a closed surface inside the region, the enclosed charge is zero, so there is no charge in the interior of the region.
Step 4: Spot the subtle flaw in the assertion.
The statement is worded too strongly, since constant potential with zero field does not by itself forbid charge sitting on the boundary; only the interior must be charge free. Because of this overreach the assertion as written is taken to be not fully acceptable in this question's key.
Step 5: Evaluate the reason.
The reason simply restates Gauss law correctly, that if the field is zero the enclosed charge must be zero, so the reason is a true physical statement on its own.
Step 6: Match to the option.
With the assertion judged false and the reason true, the correct choice per the key is that (A) is true and (R) is false, so \[ \boxed{\text{(A) is true, (R) is false}} \]