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Question #42897

Difficulty: 8/10 | 🟢 Free

The Question

Three point charges are fixed on a circle of radius $R$ in the $xy$ -plane centered at the origin. Charge $q_1 = +q$ is located at $\theta = 0^\circ$ , $q_2 = -q$ is at $\theta = 60^\circ$ , and $q_3 = +q$ is at $\theta = 120^\circ$ . An ideal electric dipole with dipole moment $\vec{p} = p_0 \hat{i}$ is placed at the origin. What is the magnitude of the net electric force experienced by the dipole?

Options

A.
$\frac{\sqrt{43} q p_0}{8 \pi \epsilon_0 R^3}$
B.
$0$
C.
$\frac{5 q p_0}{8 \pi \epsilon_0 R^3}$
D.
$\frac{3\sqrt{7} q p_0}{8 \pi \epsilon_0 R^3}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Superposition Principle|Conservative Force Field|Vector Decomposition Ambiguity

Why This Question Is Tricky

Common Mistakes

This question weaponizes 'symmetry bias' by placing charges such that the net electric field at the origin is exactly zero.

Students relying on superficial symmetry will incorrectly conclude that a zero field implies zero force on the dipole (Option B).

However, the force on an ideal dipole depends on the gradient of the electric field ( $\vec{F} = (\vec{p} \cdot \nabla)\vec{E}$ ), not the field itself.

Furthermore, the problem forces rigorous vector decomposition of the field gradients.

A secondary trap awaits students who attempt the gradient calculation but incorrectly assume that the anti-symmetric signs of $q_2$ and $q_3$ cause their gradient components to symmetrically cancel, leading to Option C.

The non-orthogonal $60^\circ/120^\circ$ configuration ensures that standard shortcut vectors fail, demanding component-wise superposition.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electric Charges and Fields - Class 12
Concept	Superposition Principle
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free