---
title: "Two small conducting spheres of masses \\(m_1\\) and \\(m_2\\) carry positive charges \\(q_1\\) and \\(q_2\\), respectively, where \\(m_1  q_2\\).  The spheres are suspended from a single pivot by light insulating threads of equal length, coming to static equilibrium with thread angles \\(\\theta_1\\) and \\(\\theta_2\\) relative to the vertical.  Even when the charges are interchanged so that sphere 1 carries \\(q_2\\) and sphere 2 carries \\(q_1\\), the equilibrium angles remain unchanged with \\(\\theta_1 > \\theta_2\\).  Which of the following best explains why sphere 1 deflects by a greater angle than sphere 2 regardless of which sphere carries the larger charge?"
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url: "https://nerd-notes.com/ubq/124508/"
date_modified: "2026-09-28T14:08:24+00:00"
---

# Two small conducting spheres of masses \(m_1\) and \(m_2\) carry positive charges \(q_1\) and \(q_2\), respectively, where \(m_1  q_2\).

The spheres are suspended from a single pivot by light insulating threads of equal length, coming to static equilibrium with thread angles \(\theta_1\) and \(\theta_2\) relative to the vertical.

Even when the charges are interchanged so that sphere 1 carries \(q_2\) and sphere 2 carries \(q_1\), the equilibrium angles remain unchanged with \(\theta_1 > \theta_2\).

Which of the following best explains why sphere 1 deflects by a greater angle than sphere 2 regardless of which sphere carries the larger charge?

Two small conducting spheres of masses \(m_1\) and \(m_2\) carry positive charges \(q_1\) and \(q_2\), respectively, where \(m_1 < m_2\) and \(q_1 > q_2\).

The spheres are suspended from a single pivot by light insulating threads of equal length, coming to static equilibrium with thread angles \(\theta_1\) and \(\theta_2\) relative to the vertical.

Even when the charges are interchanged so that sphere 1 carries \(q_2\) and sphere 2 carries \(q_1\), the equilibrium angles remain unchanged with \(\theta_1 > \theta_2\).

Which of the following best explains why sphere 1 deflects by a greater angle than sphere 2 regardless of which sphere carries the larger charge?

![A schematic diagram showing two small spheres suspended from a single support point at the top center. A vertical dashed line extends downward from the support point. Two straight solid lines representing threads of equal length extend downward and outward from the support point: one to the left ending at a small circular sphere labeled m_1, q_1, and one to the right ending at a small circular sphere labeled m_2, q_2. The left thread makes an angle labeled \theta_1 with the vertical dashed line, and the right thread makes an angle labeled \theta_2 with the vertical dashed line, where \theta_1 is visually noticeably larger than \theta_2. A horizontal dashed line indicates that both spheres are at comparable heights. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604504-CyluQ3.jpg)

- **A.** The external electric field produced by each sphere exerts a force proportional only to the other sphere's charge, so swapping the charges causes an exchange of forces that is exactly compensated by the redistribution of electrostatic potential energy between the two hanging lengths.
- **B.** The electrostatic repulsive forces on the two spheres form an action-reaction pair of equal magnitude determined by the product \(q_1 q_2\), so horizontal and vertical force balance requires \(\tan\theta = \dfrac{F_e}{mg}\), meaning the deflection angle is determined solely by the sphere's mass.
- **C.** The stronger electric field originating from the sphere carrying the larger charge polarizes the surface of the lighter sphere more intensely, creating an asymmetric net repulsion that drives the lighter sphere farther outward regardless of charge placement.
- **D.** The system minimizes its total potential energy when the center of charge coincides with the center of mass, requiring the less massive sphere to displace through a larger horizontal distance to balance the gravitational torque about the pivot.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124508/*