Imagine a charged particle (like an electron or a proton) speeding along a straight line. If we place it in a uniform magnetic field that is perpendicular to its direction of motion, the particle will feel a sideways push that changes its path into a circle. This is because the magnetic force is always perpendicular to the velocity, so it never does work on the particle but only changes its direction.
Key Formula (Lorentz Force):
\$\mathbf{F} = q\,\mathbf{v}\times\mathbf{B}\$
When v ⟂ B, the magnitude simplifies to:
\$F = q\,v\,B\$
1️⃣ Point your thumb in the direction of the particle’s velocity v.
2️⃣ Point your index finger in the direction of the magnetic field B.
3️⃣ Your middle finger (perpendicular to both) points in the direction of the force F on a positive charge.
For a negative charge, the force is in the opposite direction.
🤓 Tip: Practice with a real magnet and a small metal ball to feel the push!
The magnetic force acts as a centripetal force, keeping the particle in a circle. The radius of the path is given by:
\$r = \frac{m\,v}{q\,B}\$
where m is the particle’s mass.
The speed remains constant because the force is always perpendicular to the velocity (no work done), but the direction keeps changing.
In a cyclotron, charged particles are accelerated in a circular path by a magnetic field. As they gain energy, their speed increases, so the radius expands until they reach the outer wall and are extracted for use in medicine or research.
🎯 Analogy: Think of a merry‑go‑round that keeps spinning because of a constant sideways push, never speeding up or slowing down.
| Symbol | Meaning | Units |
|---|---|---|
| \$q\$ | Charge of particle | Coulombs (C) |
| \$v\$ | Velocity of particle | m s⁻¹ |
| \$B\$ | Magnetic field strength | Tesla (T) |
| \$F\$ | Magnetic force | Newton (N) |
| \$m\$ | Mass of particle | kg |