magnets and force

Question

The Electrons in a beam are moving at 2.5×108 m/s in an electric field of 19000 N/C. What value must the magnetic field have if the electrons pass through the crossed fields undeflected?

Answer in units of µT.

Answer 1

The electric field must create a force on the electron which is equal in magnitude but opposite in direction to the magnetic force.

The force on a moving electron due to a magnetic field is given by qvB where q is the charge, v is the velocity and B is the magnetic field.

The force on an electron due to an electric field is given by qE where E is the Electric Field

We can now write qvB = qE

As the charges cancel, it simplifies to

vB=E therefore we get B=E/v