STATEMENT-1`:` If potential energy of a dipole in stable equilibrium position is zero, its potential energy is unstable equilibrium position will be 2pE, where p and E represent the dipole moment and electric field respectively
and
STATEMENT-2 `:` The potential energy of a dipole is minimum in stable equilibruim positioni and maximum in unstable equilibrium position.

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1
B. Statement-1 is True, Statement-2 is True, Statement-2 is NOT a correct explanation for Statement-1
C. Statement-1 is True, Statement-2 is False
D. Statement-1 is False , Statement-2 is True

Answer

To solve the problem, we need to analyze both statements regarding the potential energy of a dipole in electric fields.

### Step 1: Understanding Potential Energy of a Dipole
The potential energy (U) of a dipole in an electric field (E) is given by the formula:
\[ U = -\vec{p} \cdot \vec{E} \]
where \( \vec{p} \) is the dipole moment vector.

### Step 2: Analyzing Stable Equilibrium
In stable equilibrium, the dipole is aligned with the electric field. The potential energy is minimized, and the formula becomes:
\[ U_{stable} = -pE \]
If we assume that the potential energy in this position is zero, we can set:
\[ -pE = 0 \]
This implies that either \( p \) or \( E \) must be zero, which is not typical in a dipole scenario. However, if we take the reference point where the potential energy is zero, we can analyze the unstable equilibrium.

### Step 3: Analyzing Unstable Equilibrium
In unstable equilibrium, the dipole is oriented opposite to the electric field. The potential energy is maximized, and the formula becomes:
\[ U_{unstable} = pE \]
If we consider the potential energy in stable equilibrium as zero, then the potential energy in unstable equilibrium can be expressed as:
\[ U_{unstable} = 2pE \]
This means that the potential energy in the unstable position is indeed twice that of the stable position.

### Step 4: Conclusion
Thus, we can conclude that:
- **Statement 1** is true: If the potential energy of a dipole in stable equilibrium is zero, then its potential energy in unstable equilibrium will be \( 2pE \).
- **Statement 2** is also true: The potential energy of a dipole is minimum in stable equilibrium and maximum in unstable equilibrium.

### Final Answer
Both statements are true.

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