Magnetic field to keep an electron on a circular orbit?

Question

What magnetic field is required to constrain an electron with a kinetic energy of 301 eV to a circular path of radius 0.714 m?

I have no idea... I need some help.

Answer 1

Set the centripetal force required equal to the magnetic force:

m v^2 / r = qvB

Solve for your magnetic field:

B = mv / qr

The electron's kinetic energy is:

T = 1/2 mv^2

Solve that for v (which you don't know) in terms of T (which is given):

v = sqrt (2T/m)

And plug that back into your magnetic field:

B = sqrt (2Tm) / qr

You are given the energy and radius.  You can look up the electron's charge and mass.  Plugnchug.  Note that you'll need to convert kinetic energy from eV to joules, which means multiplying it by the fundamental charge.  Or since you have an electron and they give you electron volts, you could just say they've given you the potential V = T/q in volts.

So B = sqrt (2qVm)/qr

= sqrt (2Vm / qr^2)

Answer 2

I don't think the radius should be that big?