---
title: "A small droplet of mass \\(m\\) and negative charge \\(-q\\) (where \\(q > 0\\)) travels horizontally to the right with constant speed \\(v_0\\) through a region of uniform gravitational, electric, and magnetic fields.  The gravitational field \\(\\vec{g}\\) and the electric field \\(\\vec{E}\\) are both directed vertically downward, and the field magnitudes satisfy \\(qE > mg\\).  In order for the droplet to continue moving along a straight horizontal path at constant speed, what must be the direction and magnitude of the magnetic field \\(\\vec{B}\\)?"
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url: "https://nerd-notes.com/ubq/123277/"
date_modified: "2026-09-28T11:58:04+00:00"
---

# A small droplet of mass \(m\) and negative charge \(-q\) (where \(q > 0\)) travels horizontally to the right with constant speed \(v_0\) through a region of uniform gravitational, electric, and magnetic fields.

The gravitational field \(\vec{g}\) and the electric field \(\vec{E}\) are both directed vertically downward, and the field magnitudes satisfy \(qE > mg\).

In order for the droplet to continue moving along a straight horizontal path at constant speed, what must be the direction and magnitude of the magnetic field \(\vec{B}\)?

A small droplet of mass \(m\) and negative charge \(-q\) (where \(q > 0\)) travels horizontally to the right with constant speed \(v_0\) through a region of uniform gravitational, electric, and magnetic fields.

The gravitational field \(\vec{g}\) and the electric field \(\vec{E}\) are both directed vertically downward, and the field magnitudes satisfy \(qE > mg\).

In order for the droplet to continue moving along a straight horizontal path at constant speed, what must be the direction and magnitude of the magnetic field \(\vec{B}\)?

![A schematic diagram showing a small solid dark circle labeled \(-q\) and \(m\) in the center. A single horizontal arrow extends to the right from the droplet, labeled \(v_0\). Directly to the left, a coordinate reference is shown with a vertical arrow pointing upward labeled \(+y\) and a horizontal arrow pointing right labeled \(+x\). A downward-pointing vertical arrow on the far left is labeled \(g\). Four parallel downward-pointing vertical arrows are distributed horizontally across the upper region, each labeled \(E\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790596684-gJeG7i.jpg)

- **A.** Out of the page, with magnitude \(B = \dfrac{qE + mg}{qv_0}\)
- **B.** Out of the page, with magnitude \(B = \dfrac{qE - mg}{qv_0}\)
- **C.** Into the page, with magnitude \(B = \dfrac{qE + mg}{qv_0}\)
- **D.** Into the page, with magnitude \(B = \dfrac{qE - mg}{qv_0}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/123277/*