How do charged particles move when subject to electric and magnetic forces?
A charged particle placed in an electric field accelerates along the field lines (or against them, for negative charges). A charged particle moving through a magnetic field experiences a force perpendicular both to its velocity and to the field — which means it does no work on the particle, so the speed stays constant but the direction changes. The result is circular motion in a uniform magnetic field: the basis of cyclotrons, mass spectrometers, and the aurora borealis.
When electric and magnetic forces are balanced — qE = qvB — only particles with a specific speed pass straight through: this is a velocity selector. Mass spectrometers combine a velocity selector with a magnetic field to separate ions by their charge-to-mass ratio, enabling precise atomic mass measurements and isotope identification. The same physics governs cathode ray tubes, particle accelerators, and medical PET scanners.
An electron enters a uniform magnetic field of 0.05 T perpendicular to its velocity of 2.0 × 10⁶ m s⁻¹. Show that the electron travels in a circle, and calculate its radius. (Electron mass: 9.11 × 10⁻³¹ kg; charge: 1.6 × 10⁻¹⁹ C)
Key equations
Force on moving charge: F = qvB sinθ
Circular motion in B-field: qvB = mv²/r → r = mv/qB
Force on current-carrying conductor: F = BIL sinθ
Force per unit length between parallel wires: F/L = μ₀I₁I₂/(2πr)
Velocity selector condition: qE = qvB → v = E/B
What students must understand
Motion of a charged particle in a uniform electric field: constant acceleration along field lines
Motion of a charged particle in a uniform magnetic field: circular motion; no work done; constant speed
Combined perpendicular E and B fields: velocity selector condition v = E/B
Force magnitude and direction: F = qvB sinθ (use the right-hand rule or Fleming's left-hand rule)
Force on a current-carrying conductor: F = BIL sinθ
Force between parallel current-carrying wires: F/L = μ₀I₁I₂/(2πr); same direction → attractive
Charge-to-mass ratio determination from circular orbit in a magnetic field
Linking questions
How does rotation apply to charged particles in a cyclotron? → A.4 Rigid Body Mechanics
How does the Lorentz force relate to electric and magnetic fields? → D.2
Video Support
Flipping Physics
Magnetic Fields and Magnetic Forces on Moving ChargesMagnetic Force Direction (Right-Hand Rule)
The Organic Chemistry Tutor
Magnetic Force on a Moving Charge In a Magnetic FieldMagnetic Force on a Current Carrying WireMagnetic Field of a Moving Charge, Proton, Right Hand Rule - Physics & Electromagnetism
Michel van Biezen
Physics 43 Magnetic Forces on Moving Charges (1 of 26) An Introduction - Determine DirectionPhysics 43 Magnetic Forces on Moving Charges (21 of 26) The Cyclotron
WNY Tutor — worked problems
A proton travels through uniform magnetic and electric fieldsAn electron moves through a uniform magnetic field