Force Experienced by an Electron moving in a Magnetic Field

Let b be the magnetic flux density acting perpendicular to the plane of the paper inwards. An electron of charge e when it is not moving, experiences no force in a magnetic field, But when it moves, it is equivalent to a current.
Let the electron move with a velocity v in a direction perpendicular to the magnetic field. Let the electron move a distance l in time t.
Then        t = l/v
Current = I = rate of flow of charge = e/t  = ev/l

Let the electrons be moving with a uniform spacing of l. Then, each electron can be considered to be equivalent to be equivalent to a conductor of length l carrying a current ev/l.

. : Force experienced by the electron,
    F = ilB = ev/l . lb = evB

The force is perpendicular to both v and B. This force is called the Lorentz force. It acts only when the particle is moving.