Magnetic forces and induction
Magnetism acts only on moving charge, and a changing magnetic flux is paid back with voltage — that trade runs every generator.
Magnetic force
A charge moving through a magnetic field feels a force perpendicular to both its velocity and the field: F = qvB sin(theta), biggest when the motion is perpendicular to B and zero when parallel. A current-carrying wire gets the same treatment, F = BIL sin(theta). Point your fingers along v or the current, curl them toward B, and your thumb gives the force on positive charge — the right-hand rule.
F = qvB\sin\thetaFaraday and Lenz
Faraday's law says a changing magnetic flux through a loop drives an EMF equal to the flux change per turn times the number of turns. Lenz's law is the minus sign: the induced current flows so its own field opposes the change in flux. That opposition is why generators demand mechanical work and why induction cannot deliver free energy.
\mathcal{E} = -N\frac{d\Phi_B}{dt}Worked example
A 100-turn coil with area 0.010 m^2 sits in a 0.50 T field that drops to zero in 0.20 s. The flux per turn changes by (0.50)(0.010) = 5.0e-3 Wb, so the EMF is 100*(5.0e-3)/0.20 = 2.5 V while the field decays. By Lenz's law the induced current flows so its own field keeps pointing the way the external field used to — opposing the decrease.
\mathcal{E} = N\frac{\Delta\Phi}{\Delta t} = \frac{(100)(5.0\times 10^{-3})}{0.20} = 2.5\ \text{V}Flashcard
Force on a moving charge in a magnetic field
Check your understanding
A straight wire 0.50 m long carries 4.0 A perpendicular to a 0.30 T magnetic field. What force does it feel?