A charge moving through electric and magnetic fields experiences a force equal to the electric force plus a magnetic force perpendicular to both its velocity and the field.
v to the right, B into the page → F straight up (for a positive charge).
F = q(E + v × B)
F
force on the charge (newtons)
q
charge (coulombs)
E
electric field (volts per metre)
v
velocity of the charge (metres per second)
B
magnetic field (teslas)
In plain English: The electric field pushes a charge along the field; the magnetic field pushes it sideways — always at right angles to its motion, so it steers the charge but never speeds it up.
Where you'll meet it: The force that spins every motor (F = BIL on a wire), deflected the beam in CRT TVs, bends particle paths in mass spectrometers, and generates the voltage in Hall-effect sensors.