Physic Labs

Electricity and magnetism

The Lorentz force

Observe the trajectory of a charged particle in a magnetic field while varying B and the particle speed. Verify F=qvBsin⁡θF=qvB\sin\theta and the force direction from the left-hand rule.

High school

Equipment

  • 3D model of a charged particle in a uniform magnetic field
  • Magnetic-field and Angle/Speed sliders
  • Orbit-radius readout and Pause button

Procedure

  1. Vary B at fixed speed

    In panel 1, hold «Angle/Speed» fixed and drag «Magnetic field» from 10 to 100. Watch the path curve more and read the radius: the Lorentz force is perpendicular to velocity, so it bends the motion without changing |v| — the orbit is a circle.

  2. Verify the Larmor radius

    For two B values and two speeds, read the radius r and check r=mv/(qB)r=mv/(qB): r grows with v and shrinks with B. Use «Pause» to time a revolution and notice the period T=2πm/(qB)T=2\pi m/(qB) is independent of v.

  3. Check the angular dependence

    Use «Angle/Speed» to change the angle between v and B. At θ = 90° the force peaks at F=qvBF=qvB and the orbit closes into a circle; as θ shrinks, the component parallel to B is unperturbed and the path opens into a helix — consistent with F=qvBsin⁡θF=qvB\sin\theta.

  4. Predict force direction and charge sign

    In panel 2, watch the orbit's bending direction and apply the left-hand rule to infer B's direction or the charge sign. Reverse the charge (current direction), predict the new bend before running — the force flips when q changes sign.

Simulation

Experiment history

Nineteenth-century experiments on cathode rays opened the way to the force on a moving charge: James Clerk Maxwell already wrote the v⃗×B⃗\vec v\times\vec B term in his field equations, and Oliver Heaviside cast it as the force on a charge (1889). Hendrik Antoon Lorentz assembled the complete form F⃗=q(E⃗+v⃗×B⃗)\vec F=q(\vec E+\vec v\times\vec B) in 1895 within his electron theory — whence the name «Lorentz force». In 1897 J.J. Thomson measured the e/m ratio of cathode rays by balancing electric and magnetic deflections — the first evidence for a subatomic particle. Magnetic bending then became the backbone of mass spectrometry (Aston, 1919), the cyclotron (Lawrence, 1932), and every modern accelerator.

Related physicists

Michael FaradayJames Clerk MaxwellJoseph John Thomson

Related library topics

The Lorentz force