An electric dipole is plced at an angle of `30^(@)` to a nonuniform electric field. The dipole will experience

Options

A. a translational force only in the direction of the field
B. a translational force only in a direction normal to the direction of the field
C. a torque as well as a translational force
D. a torque only

Answer

To solve the problem of an electric dipole placed at an angle of \(30^\circ\) to a non-uniform electric field, we need to analyze the forces and torques acting on the dipole. Here's a step-by-step breakdown:

### Step 1: Understand the Electric Dipole
An electric dipole consists of two equal and opposite charges, \(+q\) and \(-q\), separated by a distance \(d\). The dipole moment \( \vec{p} \) is given by:
\[ \vec{p} = q \cdot d \]
The dipole moment is a vector quantity that points from the negative charge to the positive charge.

### Step 2: Analyze the Non-Uniform Electric Field
In a non-uniform electric field, the electric field strength \( \vec{E} \) varies from point to point. This means that the forces acting on the two charges of the dipole will not be equal and opposite.

### Step 3: Calculate the Forces on the Dipole
The force on the positive charge \(+q\) in the electric field \( \vec{E} \) is:
\[ \vec{F}_+ = +q \vec{E} \]
The force on the negative charge \(-q\) is:
\[ \vec{F}_- = -q \vec{E} \]
Since the electric field is non-uniform, the forces will be different. The net force \( \vec{F}_{net} \) acting on the dipole is:
\[ \vec{F}_{net} = \vec{F}_+ + \vec{F}_- = +q \vec{E}_+ - q \vec{E}_- \]
where \( \vec{E}_+ \) and \( \vec{E}_- \) are the electric fields at the positions of the positive and negative charges, respectively.

### Step 4: Determine the Torque on the Dipole
The torque \( \tau \) acting on the dipole in an electric field is given by:
\[ \tau = \vec{p} \times \vec{E} \]
The torque tends to align the dipole moment with the electric field. Since the dipole is at an angle of \(30^\circ\) to the field, it will experience a torque that can be calculated as:
\[ \tau = pE \sin(30^\circ) = \frac{1}{2} pE \]

### Step 5: Conclusion
In a non-uniform electric field, the dipole experiences both a net translational force (due to the difference in forces on the two charges) and a torque (which tends to align the dipole with the field). Therefore, the correct answer to the question is that the dipole will experience both torque and translational force.

### Final Answer
The dipole will experience a torque as well as a translational force.

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