Question

The electron of hydrogen atom moves along a circular path of radius 0.5 * 10 -10 m (i) with a speed of 4.0 * 10^ 6 m/s (ii) with a frequency of 6.8* 10^15 Hz calculate the magnetic field at the center of the loop in both cases

Answer 1

Magnetic field at the center of the loop will be given by

$B = \frac{\mu_o i}{2R}$

here

i = current in the loop due to revolution of charge

now here we have

$i = \frac{dq}{dt} = e*f$

here

e = electronic charge

f = frequency

$i = 1.6*10^{-19}*6.8*10^{15}$

$i = 1.09*10^{-3}A$

now magnetic field at the center of the loop will be

$B = \frac{4\pi * 10^{-7} * 1.09*10^{-3}}{2*0.5*10^{-10}}$

$B = 13.7 T$

so magnetic field will be 13.7 T at its center