Why does the magnetic field only change the particle's direction and not its speed?

The magnetic force is always perpendicular to the particle's velocity (v × B). Since work done by a force is F · v, a perpendicular force does zero work. Therefore, the magnetic force cannot change the particle's kinetic energy or speed; it only provides centripetal acceleration, changing the direction of motion.

What is the real-world significance of the E×B drift?

E×B drift is crucial in many plasma and space physics contexts. It explains how charged particles and entire plasma clouds move in crossed fields, such as in the Earth's magnetosphere (causing auroral phenomena) and in laboratory devices like Hall-effect thrusters for spacecraft propulsion and certain designs of magnetic confinement fusion reactors.

Does the simulator's 2D model miss important 3D effects?

Yes, this is a key simplification. In 3D, if a particle has a velocity component parallel to the magnetic field (v_∥), it will move in a helix along the field lines. Our 2D model assumes B is perfectly perpendicular to the plane, so v_∥ is zero, showing only the motion perpendicular to B (the cyclotron and drift motion).

Why do positive and negative particles sometimes drift in the same direction in the E×B drift?

This is a non-intuitive result of the Lorentz force. While the electric force pushes positive and negative charges in opposite directions, the resulting circular motions in the magnetic field are also in opposite senses. These two effects combine such that the average drift velocity, v_d = (E × B)/B², is identical for both charge species, a fundamental property of E×B drift.

Particle in E and B Fields

The motion of a charged particle in combined electric and magnetic fields is governed by the Lorentz force law: F = q(E + v × B). This fundamental equation dictates that the force on a particle with charge q and velocity v is the vector sum of an electric force, qE, which acts in the direction of the electric field E, and a magnetic force, q(v × B), which is perpendicular to both the particle's instantaneous velocity and the magnetic field B. This simulator visualizes the resulting trajectories by numerically solving Newton's second law, F = m a, for a single particle in two dimensions. The model assumes uniform, static E and B fields that are perpendicular to the plane of motion, allowing for clear visualization of key phenomena. Students can observe pure cyclotron motion (circular orbits) when only a magnetic field is present, with a cyclotron frequency ω_c = qB/m and radius r = mv/(|q|B). When both fields are present, the trajectory becomes a superposition of rapid cyclotron motion and a slower, constant drift velocity. A particularly important case is the E×B drift, where a uniform electric field perpendicular to a uniform magnetic field causes the particle's guiding center to drift with a velocity v_d = (E × B) / B², independent of the particle's charge and mass. The simulator uses simplified, dimensionless units for clarity, focusing on the qualitative and geometric nature of the motion rather than specific numerical scales. By manipulating the particle's initial velocity and the field strengths, learners can explore how these parameters influence the orbit's shape, size, and drift, building intuition for applications ranging from mass spectrometers and particle accelerators to the confinement of plasma in fusion devices.

Who it's for: Undergraduate physics and engineering students studying electromagnetism, particularly courses covering charged particle dynamics and plasma physics fundamentals.

Key terms

Lorentz Force
Cyclotron Motion
E×B Drift
Guiding Center
Magnetic Force
Charged Particle Trajectory
Uniform Magnetic Field
Cross Product

Live graphs

How it works

A non-relativistic point charge in uniform electric and magnetic fields obeys the Lorentz force law F = q(E + v × B). In the plane perpendicular to B, this produces cyclotron motion when E vanishes, parabolic bending when B vanishes, and steady E×B drift when both are present. This simulation uses a consistent reduced unit system with scaled time so trajectories are easy to see; compare the measured |v|(t) to expectations for pure magnetic deflection (speed constant).

Key equations

m a = q(E + v × B)

ω_c = |q|B/m · R = mv⊥/(|q|B)

Frequently asked questions

Why does the magnetic field only change the particle's direction and not its speed?: The magnetic force is always perpendicular to the particle's velocity (v × B). Since work done by a force is F · v, a perpendicular force does zero work. Therefore, the magnetic force cannot change the particle's kinetic energy or speed; it only provides centripetal acceleration, changing the direction of motion.
What is the real-world significance of the E×B drift?: E×B drift is crucial in many plasma and space physics contexts. It explains how charged particles and entire plasma clouds move in crossed fields, such as in the Earth's magnetosphere (causing auroral phenomena) and in laboratory devices like Hall-effect thrusters for spacecraft propulsion and certain designs of magnetic confinement fusion reactors.
Does the simulator's 2D model miss important 3D effects?: Yes, this is a key simplification. In 3D, if a particle has a velocity component parallel to the magnetic field (v_∥), it will move in a helix along the field lines. Our 2D model assumes B is perfectly perpendicular to the plane, so v_∥ is zero, showing only the motion perpendicular to B (the cyclotron and drift motion).
Why do positive and negative particles sometimes drift in the same direction in the E×B drift?: This is a non-intuitive result of the Lorentz force. While the electric force pushes positive and negative charges in opposite directions, the resulting circular motions in the magnetic field are also in opposite senses. These two effects combine such that the average drift velocity, v_d = (E × B)/B², is identical for both charge species, a fundamental property of E×B drift.