When an electron passes through the magnetic field of a horseshoe magnet, the electron's direction is changed.
Path of an electron in a magnetic field
The force (F) on wire of length L carrying a current I in a magnetic field of strength B is given by the equation:
F = BIL
But Q = It and since Q = e for an electron and v = L/t you can show that :
Magnetic force on an electron = BIL = B[e/t][vt] = Bev where v is the electron velocity
In a magnetic field the force is always at right angles to the motion of the electron (Fleming's left hand rule) and so the resulting path of the electron is circular.
Therefore :
Magnetic force = Bev = mv2/r = centripetal force
v = [Ber]/m
and so you can see from these equations that as the electron slows down the radius of its orbit decreases.
If the electron enters the field at an angle to the field direction the resulting path of the electron (or indeed any charged particle) will be helical. Such motion occurs above the poles of the Earth where charges particles from the Sun spiral through the Earth's field to produce the aurorae.
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