An electron of kinetic energy 45 kev moves in a counter-clockwise circular orbit perpendicular to a magnetic field of 0.325 t. calculate the acceleration of the electron.

Let's convert the kinetic energy of the electron from keV to Joule:

And from the kinetic energy, we find the velocity of the electron:

where  is the electron mass. Re-arranging the formula, we find v:


The magnetic force acting on the electron is:
F=qvB
where 
is the electron charge
is the electron velocity
B=0.325 T is the magnetic field.

For Newton's second law, we also have that F=ma, so we can rewrite the equation as

and so from this, we can find the acceleration (which is a centripetal acceleration, because the electron is moving by circular motion):