# Proton in a magnetic field

1. Homework Statement

I have a circular magnetic field and a proton (A) a distance Ra from the center of the circle. The magnetic field is traveling into the page and is decreasing at some rate B(t). I have the radius of the circle Rb.

The question is that when the proton is released, what happens to the proton?

2. Homework Equations

F = qv x b
Right Hand Rule

3. The Attempt at a Solution

I'm pretty sure that with a changing magnetic field, it will create an induced current/magnetic field that will exert a force on it. Its not a mathematical problem necessarily i just need to know what happens to the proton. in the midst of a changing magnetic field.

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is the proton moving?

well i assume it starts as stationary because the problems says "when the proton is released". so no i dont think theres a velocity vector to it.

Doc Al
Mentor
The changing magnetic field will create an electric field (induced EMF).

so the induced EMF (E) will exert a force on the proton F=qE then?

So... i use faraday's law to determine the E and just multiply it by q?

Doc Al
Mentor
so the induced EMF (E) will exert a force on the proton F=qE then?

So... i use faraday's law to determine the E and just multiply it by q?
Right. But as soon as it starts moving there will be a magnetic force on the proton as well.

so at the end of the day.

the induced emf (the E field) will exert a force on the proton, but as the proton moves, there will be a magnetic force on the proton (cross product of its velocity and the magnetic field)?

in terms of vectors then...can i expect it to move wherever the resultant of the summed E and B field vector?

Doc Al
Mentor
so at the end of the day.

the induced emf (the E field) will exert a force on the proton, but as the proton moves, there will be a magnetic force on the proton (cross product of its velocity and the magnetic field)?
Sounds good.

in terms of vectors then...can i expect it to move wherever the resultant of the summed E and B field vector?
You can expect that the net force on it will be the vector sum of the electric and magnetic forces.