Question

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.)

Answer 1

`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.