Electric field inside a conductor can be zero only, if potential inside the conductor is

Options

A. If both assertion and reason are ture and reason is the correct explanation of assertion.
B. If both assertin and reason are ture but reason is not the correct explanation of assertion .
C. If assertion is true but reason is false.
D. If both assertion and reason are false.

Answer

To solve the question, "Electric field inside a conductor can be zero only if potential inside the conductor is...", we will follow these steps:

### Step 1: Understand the relationship between electric field and potential
The electric field (E) is related to the electric potential (V) by the equation:
\[ E = -\frac{dV}{dx} \]
This equation indicates that the electric field is the negative gradient of the electric potential.

### Step 2: Analyze the condition for zero electric field
If the electric field inside the conductor is zero, we can set:
\[ E = 0 \]
Substituting this into the equation gives:
\[ 0 = -\frac{dV}{dx} \]

### Step 3: Interpret the result of the equation
From the equation \( 0 = -\frac{dV}{dx} \), we can conclude that:
\[ \frac{dV}{dx} = 0 \]
This means that the derivative of the potential with respect to position is zero.

### Step 4: Conclude about the potential
If the derivative of the potential is zero, it implies that the potential (V) is constant throughout the conductor. Therefore, the potential does not change with position inside the conductor.

### Final Answer
The electric field inside a conductor can be zero only if the potential inside the conductor is constant.

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