An electron field of moment p is placed in a uniform electric field E. Then,
(i) the torque on the dipole is `pxx E`
(ii) the potential energy of the system is `p.E`
(iii) the resultant force on the dipole is zero.

Options

A. (i),(ii) and (iii) are correct
B. (i) and (iii) are correct and (ii) is wrong
C. Only (i) is correct
D. (i) and (ii) are correct and (iii) is wrong

Answer

To solve the problem, we will analyze each statement regarding an electric dipole placed in a uniform electric field.

### Step-by-Step Solution:

1. **Understanding the Electric Dipole**:
An electric dipole consists of two equal and opposite charges (+q and -q) separated by a distance 'd'. The dipole moment \( \mathbf{p} \) is defined as:
\[ \mathbf{p} = q \cdot \mathbf{d} \]
where \( \mathbf{d} \) is a vector pointing from the negative charge to the positive charge.

2. **Torque on the Dipole**:
The torque \( \mathbf{\tau} \) experienced by a dipole in a uniform electric field \( \mathbf{E} \) is given by the cross product of the dipole moment and the electric field:
\[ \mathbf{\tau} = \mathbf{p} \times \mathbf{E} \]
This means that the first statement, which states that the torque on the dipole is \( p \times E \), is correct.

3. **Potential Energy of the Dipole**:
The potential energy \( U \) of a dipole in an electric field is given by:
\[ U = -\mathbf{p} \cdot \mathbf{E} \]
This indicates that the potential energy is negative when the dipole is aligned with the electric field. Therefore, the second statement, which claims that the potential energy is \( \mathbf{p} \cdot \mathbf{E} \), is incorrect. The correct expression includes a negative sign.

4. **Resultant Force on the Dipole**:
In a uniform electric field, the forces acting on the two charges of the dipole are equal in magnitude but opposite in direction. The force on the positive charge is \( +q\mathbf{E} \) and the force on the negative charge is \( -q\mathbf{E} \). Thus, the net force \( \mathbf{F}_{\text{net}} \) on the dipole is:
\[ \mathbf{F}_{\text{net}} = +q\mathbf{E} + (-q\mathbf{E}) = 0 \]
This confirms that the third statement, which states that the resultant force on the dipole is zero, is correct.

### Summary of Statements:
- (i) The torque on the dipole is \( \mathbf{p} \times \mathbf{E} \) - **Correct**
- (ii) The potential energy of the system is \( \mathbf{p} \cdot \mathbf{E} \) - **Incorrect** (it should be \( -\mathbf{p} \cdot \mathbf{E} \))
- (iii) The resultant force on the dipole is zero - **Correct**

### Conclusion:
The correct statements are (i) and (iii). The second statement is incorrect.