Magnetism

Force on Moving Charges

Magnetic fields (in teslas) exert force only on moving charges: $F = qvB\sin\theta$ The force is maximal when velocity is perpendicular to the field and zero when parallel; the right-hand rule gives its direction (reversed for negative charges). Because the force is always perpendicular to velocity, it changes direction but never speed, and does no work.

Circular Motion in a Field

A charge entering a uniform field perpendicular to its motion travels in a circle where the magnetic force is the centripetal force: $r = \frac{mv}{qB}$ Heavier or faster particles curve less; stronger fields and larger charges bend them more — the operating principle of mass spectrometers.

Currents and Induction

A current-carrying wire feels $F = ILB\sin\theta$ and itself creates a circulating magnetic field (thumb along current, fingers curl with the field). Faraday's law states that a changing magnetic flux induces an EMF, and Lenz's law directs the induced current to oppose the change — the basis of generators and transformers.

Key Takeaways

• No charge motion, no magnetic force; parallel motion also gives zero force.
• Magnetic forces do no work — speed and kinetic energy stay constant.
• $r = mv/qB$ separates ions by mass-to-charge ratio.
• Induction requires changing flux; steady fields induce nothing.