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

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 maximized, we can follow these steps:

### Step 1: Understand the Torque on an Electric Dipole
The torque (\(\vec{\tau}\)) experienced by an electric dipole (\(\vec{P}\)) in a uniform electric field (\(\vec{E}\)) is given by the vector cross product:
\[ \vec{\tau} = \vec{P} \times \vec{E} \]
The magnitude of the torque can be expressed as:
\[ \tau = P E \sin \theta \]
where \( \theta \) is the angle between the dipole moment vector (\(\vec{P}\)) and the electric field vector (\(\vec{E}\)).

### Step 2: Analyze the Sine Function
To maximize the torque, we need to maximize the term \( \sin \theta \). The sine function reaches its maximum value of 1 when:
\[ \sin \theta = 1 \]

### Step 3: Determine the Angle
The sine function equals 1 at:
\[ \theta = 90^\circ \]
This means that the angle between the dipole moment vector (\(\vec{P}\)) and the electric field vector (\(\vec{E}\)) must be \(90^\circ\) for the torque to be maximized.

### Step 4: Conclusion
Thus, the torque on the electric dipole will be maximum when:
\[ \theta = 90^\circ \]

### Final Answer
The angle between the electric dipole moment \(\vec{P}\) and the electric field \(\vec{E}\) at which the torque is maximum is:
\[ \theta = 90^\circ \]