Problem 61 - A Complete Resource Book in Physics for JEE Main

Question

An electric dipole is placed at an angle of \(30^{\circ}\) to a non-uniform electric field. The dipole will experience (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.

Step-by-Step Solution

Answer

An electric dipole placed at an angle of \(30^{\circ}\) to a non-uniform electric field will experience both a torque and a translational force. Therefore, the correct answer is (C) a torque as well as a translational force.

Step 1: Define the electric dipole and electric field

An electric dipole is a pair of equal and opposite charges (\(+q\) and \(-q\)) separated by a distance 'd.' The dipole moment 'p' is given by: \[p = qd\] A non-uniform electric field has a variable field strength and direction in different parts of the field. The electric field strength can be represented as: \[E(x,y,z)\]

Step 2: Define the torque experienced by the dipole

When an electric dipole is placed in an electric field, the torque 'τ' experienced by the dipole is given by: \[\tau = p \times E \sin{\theta}\] where θ is the angle between the dipole moment and the electric field. Given that our dipole is placed at an angle of θ = \(30^{\circ}\) (or \(\pi/6\) radians), we can calculate the torque experienced: \[\tau = p \times E \sin{30^{\circ}}\] Since θ is non-zero, there will be a nonzero torque experienced by the dipole.

Step 3: Determine the translational force experienced by the dipole

When an electric dipole is placed in a non-uniform electric field, the net force experienced by the dipole is the sum of the forces experienced by the individual charges: \[F_{net} = qE(+q) - qE(-q)\] This force can have both a component in the direction of the field and a component normal to the field. Since the field is non-uniform, we cannot determine the direction of the force without more information, but we know that a translational force will be experienced.

Step 4: Choose the correct answer

Based on our analysis, an electric dipole placed at an angle of \(30^{\circ}\) to a non-uniform electric field will experience both a torque and a translational force. Therefore, the correct answer is: (C) a torque as well as a translational force.