Question

Learning Goal:

To understand why charged particles move in circles perpendicular to a magnetic field and why the frequency is an invariant.

A particle of charge q and mass m moves in a region of space where there is a uniform magnetic field B⃗ =B0k^(i.e., a magnetic field of magnitude B0 in the +z direction). (Figure 1) In this problem, neglect any forces on the particle other than the magnetic force.

Part D

If the resulting trajectory of the charged particle is a circle, what is ω, the angular frequency of the circular motion?

Express ω in terms of q, m, and B0.

ω =

Answer 1

Force due to magnetic field \(=\) centripetal force

\(q v B_{0}=\frac{m v^{2}}{r}\)

\(v=r \omega\)

\(q r \omega B_{0}=m r \omega^{2}\)

\(\omega=\frac{q B_{0}}{m}\)