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: Analyze Assertion (A).
Electric field is related to electric potential by \[ \vec{E}=-\nabla V \] If the potential is constant throughout a region, then \[ \nabla V=0 \] Hence, \[ \vec{E}=0 \] Therefore, the electric field inside the region is zero.
Now, from electrostatic equilibrium conditions, if the electric field is zero everywhere inside a region, there can be no net charge enclosed within that region.
Thus, Assertion (A) is true.

Step 2: Analyze Reason (R).
According to Gauss law, \[ \oint \vec{E}\cdot d\vec{A} = \frac{Q_{\text{enc}}}{\varepsilon_0} \] If \[ \vec{E}=0, \] then electric flux through the closed surface is zero. Hence, \[ Q_{\text{enc}}=0 \] So, the reason statement is also true.

Step 3: Check whether (R) correctly explains (A).
The statement that electric field is zero follows directly from the constancy of potential: \[ \vec{E}=-\nabla V \] This part is not explained using Gauss law.
Gauss law only explains why net enclosed charge becomes zero when the electric field is zero.
Hence, although both statements are true, the reason is not the correct explanation of the complete assertion.

Step 4: Final conclusion.
Therefore, \[ \boxed{\text{Both (A) and (R) are true; (R) is not the correct explanation of (A)}} \]