# Proton in a Magnetic Field

Moneer81

## Homework Statement

A proton is placed in a uniform 1.5T magnetic field.
a. Quantify the magnitude (algebraically) of the force and torque on the proton.
b. Describe the time evolution of the proton's magnetic moment.
c. Describe how to generate a uniform 1.5T magnetic field from a 1.0 amp source over a volume of 20cm x 20cm x 40cm using coils of wire.

## The Attempt at a Solution

a. So I am assuming the proton's magnetic moment is pointing to the right, and the external magnetic field is pointing up. Then the torque on the proton will be given by:

torque = mu x B = (14.1x10^-23 J/T)(1.5T)(sin 90) = 21.15x10^-23 J

force = qV x B. Can I find the force? I don't know anything about the proton's velocity. I am just assuming it is precessing around an axis that points to the right of the page. Am I on the right track here?

b. After some time, the magnetic moment of the proton (that was initially pointing to the right of the page) will align with the magnetic field B. Since there are two different spin states, the magnetic moment can be parallel with the magnetic field (low energy) or anti-parallel (high energy). DOes that sound right?

c. OK so is there an easy way to work with a volume like that? Isn't easier to create a magnetic field in a coil or cylinder? I know that we have wrap the wire coil around the volume but what else can we say to answer that question?

Thanks for taking the time to read my post.