Force on a moving charge in a magnetic field
Consider a wire carrying a current I in a field of flux density B
(Figure 1).
We have
I= nAve = qAv where q = ne also I = q/t and F= BILsin
q
Therefore the force
on a charge q is:
F = Bqv sinq and F = Bevsinq for an electron
If the charge moves at right angles to the magnetic
field this becomes
Force on a moving charge (q): F = Bqv
For an
electron (charge e) moving at right angles to the field the formula is:
Force on a moving electron: F = Bev
Notice that if the charge is at rest there is no force
upon it due to the magnetic field
Example problem
Calculate the force on an alpha particle moving with a velocity of 2x106 ms-1 at 30o to a field of flux density 3x10-3 T.
Force = Bqv sinq = 3x10-3 x 2 x 1.6x10-19 x 2x106 = 1.92x10-16 N
