Question

For your initial values I’d like you start with, mass=3.9 velocity = 3.0 charge=9.6 magnetic field strength=0.25

Notice the text entry boxes are followed by a units multiplier so entering 3.9 for mass is really 3.9x10-25 kg, for example

1. Vary the four quantities independently tabulating the radius for example you might start with the mass. So in your lab report, you might have a table like the following v=3.0e6 m/s, q= 9.6e-16 C, B=0.25 T

m (1e-25 kg)	R (mm)
3.9	4.88
4.2	5.25
4.5
4.7
5.0

Do one table for each of these; mass, velocity, charge, and magnetic field, but document the values of the other constants for each experiment. You don’t need do a lot of points for these, but should be enough to establish a pattern.

2. Look at the trends in the tables. Make a guess of the relationship between r and q,v,B, and m. I encourage you to make plots but I am not requiring it.

3. Describe how you would derive this relationship from what you know from magnetostatics (Lorentz force law) and mechanics (Newton’s 2nd Law).

Answer 1

This is a lab experiment. So I can not help with questions 1 and 2. But I can solve question 3.

It is the radius of the circular path in the presence of a magnetic field. This circular path is the trajectory of charged particles in magnetic field. For the particles to move in a circular path the centrifugal force must balance the magnetic force on the particles so

Magnetic force,

where q, v, are charge, the velocity of the particle respectively.

From Newtons second law   

where m and a are mass and acceleration of the particle.

For circular orbits

From (1) and (2)