Torque acting on a dipole in `vec (E )` is given by:

Options

A. `p xx E`
B. zero
C. p.E
D. `E xx p`

Explanation

To find the torque acting on a dipole in an electric field \( \vec{E} \), we can follow these steps:

### Step 1: Understand the Definition of Torque on a Dipole
The torque \( \vec{\tau} \) acting on an electric dipole in an electric field is given by the formula:
\[ \vec{\tau} = \vec{p} \times \vec{E} \]
where:
- \( \vec{\tau} \) is the torque,
- \( \vec{p} \) is the dipole moment,
- \( \vec{E} \) is the electric field.

### Step 2: Analyze the Cross Product
The cross product \( \vec{p} \times \vec{E} \) indicates that the torque depends on the angle \( \theta \) between the dipole moment \( \vec{p} \) and the electric field \( \vec{E} \). The magnitude of the torque can be expressed as:
\[ |\vec{\tau}| = |\vec{p}| |\vec{E}| \sin \theta \]

### Step 3: Identify the Conditions for Torque
1. If \( \theta = 0^\circ \) (i.e., \( \vec{p} \) is aligned with \( \vec{E} \)), then \( \sin \theta = 0 \) and thus \( |\vec{\tau}| = 0 \). This means there is no torque acting on the dipole.
2. If \( \theta = 90^\circ \) (i.e., \( \vec{p} \) is perpendicular to \( \vec{E} \)), then \( \sin \theta = 1 \) and the torque is maximized.

### Step 4: Conclusion
The torque acting on a dipole in an electric field is given by:
\[ \vec{\tau} = \vec{p} \times \vec{E} \]
This indicates that the torque will be zero when the dipole is aligned with the electric field and will be maximum when it is perpendicular.