An electric dipole is placed at an angle of `30^@` to a non-uniform 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

Explanation

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 solution:

### 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 orientation of the dipole is defined by the angle it makes with the electric field.

### Step 2: Analyze the Electric Field
The problem states that the dipole is placed in a non-uniform electric field. A non-uniform electric field means that the strength and direction of the electric field vary with position.

### Step 3: Determine the Forces on the Charges
In a non-uniform electric field, the force acting on each charge of the dipole will be different. The force on the positive charge (+Q) will be:
\[ \vec{F_+} = +Q \vec{E_+} \]
And the force on the negative charge (-Q) will be:
\[ \vec{F_-} = -Q \vec{E_-} \]
Where \( \vec{E_+} \) and \( \vec{E_-} \) are the magnitudes of the electric field at the positions of +Q and -Q, respectively.

### Step 4: Analyze the Resultant Force
Since the electric field is non-uniform, \( \vec{E_+} \) is not equal to \( \vec{E_-} \). Therefore, the forces \( \vec{F_+} \) and \( \vec{F_-} \) will not cancel each other out. The net force \( \vec{F_{net}} \) acting on the dipole can be expressed as:
\[ \vec{F_{net}} = \vec{F_+} + \vec{F_-} \]
This net force will cause translational motion of the dipole.

### Step 5: Analyze the Torque on the Dipole
In addition to the translational force, the dipole will also experience a torque due to the non-uniform electric field. The torque \( \vec{\tau} \) acting on the dipole can be expressed as:
\[ \vec{\tau} = \vec{p} \times \vec{E} \]
This torque will tend to align the dipole with the electric field.

### Conclusion
Thus, the dipole will experience both translational motion due to the net force and torque due to the non-uniform electric field. Therefore, the final answer is that the dipole will experience both translational motion and torque.

### Final Answer
The dipole will experience both translational motion and torque.

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