Question

Two species of singly charged positive ions of masses 20x10^-27 kg and 23.4x10^-27 kg enter a magnetic field at the same location with a speed of 1x10^5 m/s. If the strength of the field is .2 T, and they move perpendicularly to the field, find their distance of separation after they complete one half of their circular path. (answer: 2.12 cm)

I am stump. How do I solve this problem with what I am given? Thanks!

Answer 1

After entering the magnetic field, the two particles move in circles with different radii, R1 and R2. After each has moved 1/2 orbit, their paths will be separated by 2 (R1 - R2).

Use the relationship between R and B, e, m and V.

e V B = m V^2/R

R = m V/(e B)
R1 = 0.0625 m = 6.25 cm
R2 = 0.0732 m = 7.32 cm
2 (R2 - R1) = 2.14 cm

The particle in the smaller circular track will get to the half-circle position first, so they will not be quite side by side.