Question

A 500-eV electron and a 300-eV electron trapped in a uniform magnetic field move in circular paths in a plane perpendicular to the magnetic field. What is the ratio of the radii of their orbits?
a. 2.8
b. 1.7.
c. 1.3.
d. 4.0.
e. 1.0.

Answer 1

Answer:ratio of the radii of their orbits = 1.3 --- C

Explanation:

1- eV = to the kinetic energy of the electrons

and kinetic energy is given as

K.E= 1/2mv2

v = √(2E/m)----- equation 1

The force on the particles  relating to the magnetic and circular motion ( centripetal force is given as

F = magnetic force = centripetal force

F= qvB = mv2/r

qvB = mv2/r

  r = mv/qB ------ equation 2

We know from equation 1 that v = √(2E/m)

Therefore,

r = √(2mE)/qB------ equation 3

We can now say that the  ratio of the two radii of their orbits can be calculated as

r1/r2 =(√(2mE1)/qB) /(√(2mE2)/qB

Where E1 = 500-eV  and E2 = 300-eV (1- eV = to the kinetic energy of the electrons)

r1/r2 = (√(2m x500)/qB) /(√(2mx 300)/qB

Cancelling out common variables, we are left with

r1/r2 =$\sqrt{500/300}$

r1/r2= 1.29 ≈ 1.3