Magnetic field? An electron enters a region of uniform magnetic field and is observed to execute

Question

An electron enters a region of uniform magnetic field and is observed to execute circular motion, completing 178 revolutions in (delta)T = 1.15 micro seconds.

The mass of an electron is 9.10939 x 10^-31 kg and its charge is 1.60218 x 10^-19 C. Calculate the magnitude of the magnetic field in this region. Answer in units of mT.

I began to set up an equation with mv^2/r = qvB but I wasn't sure how to play it out, if that is even the correct approach.

tks.

Answer 1

For this problem you must use the formula r = mv / qB. Rearrange that to solve for the magnetic field.

178 revolutions = 1,120 rad

ω = 1,120 rad / (1.15 x 10^-6 s) = 9.74 x 10^8 rad/s

B = mv / qr = mω / q

= ((9.11 x 10^-31 kg) x (9.74 x 10^8 rad/s)) / (1.60 x 10^-19 C)

= 5.55 mT