# Quark Model of the Neutron

## Homework Statement

The neutron is a particle with zero charge. Nonetheless, it has a nonzero magnetic moment with z-component 9.66 * 10^-27 A*m^2. This can be explained by the internal structure of the neutron. A substantial body of evidence indicates that a neutron is composed of three fundamental particles called quarks: an "up" (u) quark, of charge +2e/3, and two "down" (d) quarks, each of charge - e/3. The combination of the three quarks produces a net charge of 2e/3-e/3-e/3=0. If the quarks are in motion, they can produce a nonzero magnetic moment. As a very simple model, suppose the u quark moves in a counterclockwise circular path and the d quarks move in a clockwise, circular path, all of radius r and all with the same speed v.

Determine the current due to the circulation of the u quark.

## Homework Equations

I would imagine...

qv x B = F, Il x B = F, IA x B = torque...

## The Attempt at a Solution

I'm at a complete loss. I'm not even sure how a current can be produced if there's no wire for there to be a current produced in.

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Current is the rate at which electric charge moves. This doesn't refer only to the current in a wire.

Simply

T = 2 pi r/v
I = dq/dt = delta q/delta t here
is there any chnage in q for a quark? nope!
so,
i = q(quark) v/2 pi r (since we are interested in the period - that is the time change)

Let pi = (PI) and q = q of quark

I = QV/(2(PI)r)

the rest is very easy having in mind the above. the question that is quite hard and not obvious here is since i = dq/dt ... what is the change of q and what is the change of t around one circulation? simply the charge doesn't change, so it's a constant, and the period is the time change .. imagine as a kind of a sine wave, except in reality this model does not meet all the specifications provided by the neutron characteristics. but it's a close enough start up approximation.