Question

For an electric dipole in a non-uniform electric field with dipole moment parallel to direction of the field, the force $F$ and torque $\tau$ on the dipole respectively are __________. Fill in the blank with the correct answer from the options given below.

• A. $F = 0$, $\tau = 0$
• B. $F \neq 0$, $\tau = 0$
• C. $F = 0$, $\tau \neq 0$
• D. $F \neq 0$, $\tau \neq 0$

Hint:

Remember: 1. In a uniform field: $F$ is always $0$, $\tau$ depends on the angle. 2. In a non-uniform field: $F$ is always $\neq 0$, $\tau$ depends on the angle. If $\vec{p}$ is parallel or anti-parallel to $\vec{E}$, torque is always zero!

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
An electric dipole consists of two equal and opposite charges separated by a small distance. The interaction of this dipole with an external field depends on whether the field is uniform or non-uniform, and the orientation of the dipole.

Step 2: Detailed Explanation:

• Torque ($\tau$): The formula for torque is $\vec{\tau} = \vec{p} \times \vec{E}$, or $\tau = pE\sin\theta$. In this case, the dipole moment $\vec{p}$ is parallel to the field $\vec{E}$, meaning the angle $\theta = 0^\circ$. Since $\sin(0^\circ) = 0$, the net torque is zero.
• Force ($F$): In a non-uniform field, the electric field intensity $E$ is different at the locations of the two charges ($+q$ and $-q$). Therefore, the forces $qE_1$ and $qE_2$ do not cancel each other out. This results in a non-zero net force.

Step 3: Final Answer:
In a non-uniform field with a parallel orientation, the force $F \neq 0$ and torque $\tau = 0$.