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# Direction of a Moving Particle in a Charged Particle

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1) The neutron is a particle with zero charge. However, it has a nonzero magnetic moment of 9.66 × 10−27Am2. A possible explanation for this is the circular motion of 'quarks' - fundamental subatomic particles. The neutron is believed to consist of an "up" quark with a charge of +2e/3 and two "down" quarks each of charge −e/3 (note net charge is still zero). If the quarks are in motion they can create a magnetic moment. In particular, the magnetic moment produced by a circular current is µ = IA, where I is the current and A is the area of the circle. The radius of the neutron is 1.2 × 10−15m and so this seems a reasonable estimate for the radius of the orbits. If the up quark moves around in one direction, and the down quarks move in the opposite direction, all with the same speed v how fast will they have to be moving to generate the observed magnetic moment?

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Homework Nine.

1) The neutron is a particle with zero charge. However, it has a nonzero magnetic moment of 9.66 × 10−27Am2. A possible explanation for this is the circular motion of 'quarks' - fundamental subatomic particles. The neutron is believed to consist of an "up" quark with a charge of +2e/3 and two "down" quarks each of charge −e/3 (note net charge is still zero). If the quarks are in motion they can create a magnetic moment. In particular, the magnetic moment produced by a circular current is µ = IA, where I is the current and A is the area of the circle. The radius of the neutron is 1.2 × 10−15m and so this seems a reasonable estimate for the radius of the orbits. If the up quark moves around in one direction, and the down quarks move in the opposite direction, all with the same speed v how fast will they have to be moving to generate the observed magnetic moment?

The time it takes a charge to complete a turn is:
(1.1)
Where r is the radius of rotation and v is the linear velocity.
The current of each quark is defined as:
(1.2)
Where q is the charge of the quark
Since the sign of the charges on the quarks is opposite, the fact that the top quark rotates in an opposite direction to the down quarks means that they all create a magnetic moment in the same direction.
Thus the total current is:
(1.3)
Where e is the electron's charge
The moment is given by:
(1.4)
Therefore:
(1.5)
Plugging in the numbers:

This is third of the speed of light, hence this result is not physically accurate since some relativistic corrections must be introduced. However, as a first order approximation this result is satisfactory.
The relativistic factor is:

For non-relativistic motion (see attached files).

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

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