When an electric dipole `vecp` is placed in a uniform electric field `vecE` then at what angle between `vecp` and `vecE` the value of torque will be maximum :

Options

A. `90^@`
B. `0^@`
C. `180^@`
D. `45^@`

Answer

To determine the angle at which the torque on an electric dipole in a uniform electric field is maximum, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Electric Dipole and Electric Field**:
- An electric dipole consists of two equal and opposite charges separated by a distance. The dipole moment \(\vec{p}\) is a vector quantity that points from the negative charge to the positive charge.
- A uniform electric field \(\vec{E}\) exerts forces on the charges of the dipole.

2. **Torque on the Dipole**:
- The torque \(\vec{\tau}\) experienced by the dipole in the electric field is given by the formula:
\[ \vec{\tau} = \vec{p} \times \vec{E} \]
- The magnitude of the torque can be expressed as:
\[ |\tau| = pE \sin \theta \]
- Here, \(\theta\) is the angle between the dipole moment \(\vec{p}\) and the electric field \(\vec{E}\).

3. **Maximizing the Torque**:
- To find the angle that maximizes the torque, we need to maximize the term \(\sin \theta\).
- The sine function reaches its maximum value of 1 when \(\theta = 90^\circ\).

4. **Conclusion**:
- Therefore, the torque on the dipole will be maximum when the angle between the dipole moment \(\vec{p}\) and the electric field \(\vec{E}\) is:
\[ \theta = 90^\circ \]

### Final Answer:
The value of torque will be maximum when the angle between the dipole moment \(\vec{p}\) and the electric field \(\vec{E}\) is \(90^\circ\).