An electron with a velocity of 1×10^7 ms^-1 enters a magnetic field of strength 10 T aligned perpendicular to the direction of motion of the electron. Calculate the radius of the orbital path that the electron now follows?

(mass of an electron is 9.1*10^-31 kg.)

1 Answer
May 16, 2018

r = 5.6875*10^-6 m

Explanation:

For the special case of a uniform magnetic field aligned perpendicular to the initial direction of motion we can simply equate massxcentripetal acceleration and Lorentz force:
mv^2/r = qvB
-> r= (mv)/(qB)
Now q=1.6*10^(-19) C , m=9.1*10^-31 kg , B = 10T , v =1*10^7 ms^-1 gives

r = 5.6875*10^-6 m

Note that we have ignored relativistic effects. We are at 1/30th the speed of light so they would have a non-negligible impact for a precise experiment.