Circuits & Electrical Power · A charge in a magnetic field
The force that needs motion
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The force that needs motion

A magnetic field does nothing to a charge that is sitting still. Set that charge moving and the field pushes on it — sideways, at right angles to both the motion and the field. The size of that push is F=qvBsinθF = q v B \sin\theta, read aloud F equals q v B sine theta.

Every letter, in words. FF is the magnetic force in newtons. qq is the charge in coulombs — quoted in microcoulombs on the bench, so convert. vv is the charge's speed in metres per second. BB is the magnetic flux density — the field strength — in tesla, and one tesla is a very strong field: a fridge magnet manages a few thousandths of one, an MRI bore runs to three. And θ\theta — theta — is the angle between the velocity and the field, in degrees. You will solve this for FF, for BB, and for vv.

Two things worth carrying out of this lesson. First, vv is in the numerator with nothing to soften it, so v=0v = 0 gives F=0F = 0, full stop. A stationary charge in the strongest magnet ever built feels precisely nothing. Second, the sine runs the other way from the incline's: here sin90=1\sin 90^\circ = 1, so a charge crossing the field SQUARE-ON feels the maximum force, and a charge running ALONG the field lines at θ=0\theta = 0 feels none at all. Anchor it with those two limits and you will never have to remember which trig function it is.