Does a magnetic field increase particle speed?
Will direction, speed, or both change?
- Select the magnetic experiment.
- Follow the circular trajectory in a uniform field.
- Explain how reversing charge sign would reverse the turning direction.
What to measure
Radius r, rotation period T, and constant speed.
The idea underneath
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.
F=q(v×B); r=mv/(|q|B); T=2πm/(|q|B)B in tesla; m in kg; q in C; v is perpendicular speed in m/s.
Build the argument
- Evaluate each source separately and add its vector contribution. Potential adds as a signed scalar.
- Use F = qE or F = q(v × B), then divide by mass to obtain acceleration.
- The electric model uses consistent softened potential and field with ε = 0.2 m, so values very near a source differ from ideal point charges.
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.
Applications
Electrostatic lenses steer electrons; magnetic fields separate particles by momentum and charge. Both depend on vector direction as much as field strength.
Common misconception
A field line is not generally a particle path. A negative charge accelerates opposite E. A purely magnetic force does no work.
A further investigation
What is the force if v is parallel to B?
Check your understanding
Does a pure magnetic force do work on a point charge?
- Yes
- No
Explanation
F·v=0 means kinetic energy stays constant. For v∥B the cross product and force are zero.
Model limits
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