Charge Moving in a Cyclotron Orbit
Part A = -y direction
Part B = remain perpendicular to the direction of motion
Part C = remain constant
Part D = ω = qB0/m
A particle of charge q and mass m moves in a region of space where there is a uniform magnetic field B = Bẑ (i.e., a magnetic field of magnitude B in the +z direction). In this problem, neglect any forces on the particle other than the magnetic force.
Use the right hand rule.
This force will cause the path of the particle to curve. Therefore, at a later time, the direction of the force will:
- have a component along the direction of motion
- remain perpendicular to the direction of motion
- have a component against the direction of motion
- first have a component along the direction of motion; then against it; then along it; etc.
remain perpendicular to the direction of motion
- increase over time
- decrease over time
- remain constant
Express ω in terms of q, m, and B.
This one is kind of tricky.
Fmag = qvB
Centripetal acceleration is:
ar = v2/R
and centripetal force:
Fc = mv2/R
And velocity is:
v = ωR
Since the magnetic force is the centripetal force:
Fmag = Fc
qvB = mv2/R
qB = mv/R
Substitute for velocity:
qB = mωR/R
qB = mω
ω = qB/m
Since the problem wants things in terms of B0:
ω = qB0/m