04 · The magnetic bend

Does a magnetic field increase particle speed?

Will direction, speed, or both change?

1. Select the magnetic experiment.
2. Follow the circular trajectory in a uniform field.
3. Explain how reversing charge sign would reverse the turning direction.

Measurement

Radius r, rotation period T, and constant speed.

Magnetic force is perpendicular to velocity and B. It does no work, so it bends motion without increasing speed. A known B and a measured radius can reveal m/|q|, the principle behind mass spectrometry.

B in tesla; m in kg; q in C; v is perpendicular speed in m/s.

Worked example 1

For illustrative q/m=1 C/kg, v=2 m/s and B=1.5 T, r=1.333 m.

Worked example 2

With these values T=2π/1.5=4.189 s. Doubling B halves both r and T.

What is the force if v is parallel to B?

Assumptions

Analytic circle in uniform static B. No electric field, radiation, collisions or relativity. Schematic educational values, not a manufacturing design.

University Physics Volume 2, 11.3 Motion of a Charged Particle in a Magnetic Field