an. Electron travels in a circular orbit of radius 0.5 a and frequency of 5.5*10^7hz. Findthe magnetic field produced At center
To get an answer, you have to assume that the field is uniform everywhere along the orbit, not just use a value at the center. You also must assume that the B field is perpendicular to the circular orbit.
Then use
m V^2/R = e V B
V = (e/m) B R
P (Period) = 2 pi R/V
B = (m/e)*(V/R) = (m/e)*(2 pi/P)
review:
http://en.wikipedia.org/wiki/Electron_cyclotron_resonance