Magnetic force on a current and on charged particles
PhysicsElectric & Magnetic FieldsAges 17–18
Use it with your class: students open it from a link or a QR code, with no account needed.
Next in Electric & Magnetic Fields
Wire mode: a wire segment of length l carrying current I sits in a uniform magnetic field B at angle α; the magnetic force F = BIl·sinα is found with the left-hand rule — drag to rotate the wire and watch F change. Particle mode: a charged particle (proton or electron) enters the magnetic field perpendicularly; the Lorentz force f = |q|vB makes it move in a circle of radius r = mv/(|q|B) with period T = 2πm/(|q|B). Three more modes: a velocity selector in crossed fields where only particles with v = E/B pass undeflected; a fine-beam tube where the radius of the electron circle gives e/m = 2U/(B²r²); and two parallel wires that attract or repel with F/l = μ₀I₁I₂/(2πd).
Lesson: Magnetic force on a current-carrying wire; the Lorentz force and the motion of a charged particle in a magnetic field
What it shows
A magnetic field exerts a force on moving charges. A wire of length l carrying current I in a field B feels F = BIl·sinα, and a charged particle feels the Lorentz force qvB, always perpendicular to its velocity, so it moves in a circle of radius r = mv/(|q|B). In crossed electric and magnetic fields the forces qE and qvB cancel only for v = E/B, the principle of the velocity selector. In a fine-beam tube, electrons accelerated through a voltage U circle in a known field, and the radius gives e/m = 2U/(B²r²). Two parallel currents attract or repel with F/l = μ₀I₁I₂/(2πd).
How to use
Choose a Mode. For the wire and the particle, move the B slider, drag the wire's end or swap proton and electron. In Velocity selector, set Electric field E and B until the highlighted particle passes the slit. In Fine-beam tube, change Accelerating voltage U and Coil current I, match the beam to a marker, press Record and compute e/m. In Parallel wires, vary Current I₁, Current I₂ and Separation d. The 3D view shows every setup.
Parameters you can change
- Mode Current-carrying wire, Charged particle, Velocity selector, Fine-beam tube (e/m), Parallel wires
- Magnetic flux density B 0.1–2 T
- Current I 0–10 A
- Wire length l 0.1–1 m
- Angle α between the wire and B 0–90 °
- Particle speed v 1–10 ×10⁵ m/s
- Electric field E (velocity selector) 10–1000 kV/m
- Accelerating voltage U (fine-beam tube) 100–500 V
- Coil current I (fine-beam tube) 0.5–3 A
- Current I₂ in the second wire -10–10 A
- Separation of the wires d 1–100 cm
Questions to explore
- Why does the Lorentz force never change the speed of the particle?
- If B is doubled, how does the radius of the proton's circular path change?
- How must the wire be placed in the field for the magnetic force on it to be zero?
