One way to measure the velocity and/or energy of a particle is to send it into a region containing a strong magnetic field. Any particle with charge will feel a force due to the combination of its charge, its velocity, and the magnetic field:

F = q (v x B)

As a result, the particle will move in a circle (or a helix, but let's stick with two dimensions for now).

The radius **R** of the circle can be determined from
the particle's mass, and charge, and velocity, and the
strength of the magnetic field.

Q: Derive a formula for the radius R of the circle.

In practice, physicists shoot particles of unknown speed into a magnetic field, observe the size of the curved paths they follow, and then derive the particles' speed; or, equivalently, the particles' energy.

Q: Re-arrange the above formula to solve for velocity V.

Okay, let's try using this relationship.

Physicists observe that an anti-proton
moves in a circle of radius **R = 0.0626 m**
when placed in a magnetic field of
strength **B = 0.5 Tesla.**

Q: What is the speed of the anti-proton? What is the kinetic energy of the anti-proton?

Physicists observe that another anti-proton
moves in a circle of radius **R = 12.5 m**
when placed in a magnetic field of
strength **B = 0.5 Tesla.**

Q: What is the speed of this anti-proton? What is the kinetic energy of this anti-proton?

The answer, part 1

The answer, part 2

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.