a)
The magnetic force exerted on a charged particle in motion is given by:
where
q is the charge of the particle
v is the velocity of the particle
B is the magnetic field strength
is the angle between the direction of v and B
The expression can be rewritten as
We see that the minimum magnetic field needed is the one for which , so with . In this problem, we have:
(charge of the electron)
is the force
is the electron's velocity
Substituting, we find
b)
In this case, the field is at 45 degrees to the electron's velocity, so we have
Therefore, the field strength required to obtain a force of
is the force
will be equal to