Question 4: In a uniform magnetic field B, an electron beam enters with velocity v. Write the expression for the force experienced by the electrons.

ANSWER

We know that when a charged particle moves in a magnetic field, it experiences a force. The magnitude of this force is given by

So if an electron of charge e enters a magnetic field B with velocity v at an arbitrary angle θ with the field, then it will experience a force

Here n (with cap) is a unit vector perpendicular to the plane of v and B.

If the beam consists of n electrons, then each electron will experience the same force and the total force on the beam of electrons will be

The magnitude of the force depends on the angle θ between v and B.