An electric dipole of moment `vecp` is placed normal to the lines of force of electric intensity `vecE`, then the work done in deflecting it through an angle of `180^(@)` is

Options

A. `pE`
B. `+2pE`
C. `-2pE`
D. Zero

Explanation

To find the work done in deflecting an electric dipole from an angle of \(0^\circ\) to \(180^\circ\) in an electric field, we can use the formula for the work done on a dipole in an electric field.

### Step-by-Step Solution:

1. **Understanding the Dipole Moment and Electric Field**:
- An electric dipole is characterized by its dipole moment \(\vec{p}\).
- The electric field is represented by \(\vec{E}\).

2. **Initial and Final Angles**:
- The dipole is initially aligned with the electric field, which we can consider as \(0^\circ\).
- We want to calculate the work done when it is deflected to \(180^\circ\).

3. **Work Done Formula**:
- The work done \(W\) in rotating a dipole in a uniform electric field is given by:
\[ W = -\vec{p} \cdot \vec{E} \cdot (\cos \theta_f - \cos \theta_i) \]
- Here, \(\theta_i\) is the initial angle and \(\theta_f\) is the final angle.

4. **Substituting the Angles**:
- For our case:
- \(\theta_i = 0^\circ\) (initial position)
- \(\theta_f = 180^\circ\) (final position)
- Therefore, \(\cos \theta_i = \cos 0^\circ = 1\) and \(\cos \theta_f = \cos 180^\circ = -1\).

5. **Calculating the Work Done**:
- Substitute the values into the work done formula:
\[ W = -\vec{p} \cdot \vec{E} \cdot (-1 - 1) \]
\[ W = -\vec{p} \cdot \vec{E} \cdot (-2) \]
\[ W = 2 \vec{p} \cdot \vec{E} \]

6. **Final Result**:
- Thus, the work done in deflecting the dipole through an angle of \(180^\circ\) is:
\[ W = 2 \vec{p} \cdot \vec{E} \]