What is the force on a moving charged particle in a magnetic field, and why is no work done by this force when it accelerates the particle?

A particle with electric charge q, mass m and velocity v in a constant magnetic field B experiences a force due to the field:

F = qv X B

The 'X' (cross-product) means that the force is always at 90° (perpendicular) to both the velocity and magnetic field.

If v and B point along the same line (parallel or antiparallel), the particle feels no force. Otherwise it will feel a force and accelerate (change in velocity). But acceleration doesn't necessarily mean change in speed.

Because the force is perpendicular to the velocity (direction of travel), the particle's velocity changes only in direction. The speed (magnitude of the velocity) of the particle does not change.

 

Work is defined as the force F applied to the particle times the distance s over which is it applied in the same direction.

W = Fs

(technically, W = F • ds but they took the fun out of A level physics, eh?)

Since the magnetic force is always perpendicular to the direction of travel, and hence only changes the particle's direction and not its speed, no work is done on the particle by this force:

W = 0.

N.B. The units Joules and Newton-metres are equivalent. [J] ≡ [Nm]

 

To understand further, try googling 'vector cross product', 'vector dot product'. The magnetic force is a cross product. The definition of work is a dot product. Can you guess why they are called that? :P

Answered by Rich P. Physics tutor

11452 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

Two pendulums consist of a massless rigid rod of equal length attached to a small sphere of equal radius, with one sphere hollow for one pendulum and the other solid. Each pendulum undergoes damped SHM. Which pendulum has the largest time period?


How and why does a geostationary satellite stay above the same point on the Earths surface?


Define Simple Harmonic Motion


State and derive Kepler's third law


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2024

Terms & Conditions|Privacy Policy
Cookie Preferences