Calculating change in Magnetic Dipole Moment

[iScience]

In one moment in time you have a charge going about in a circle of radius r. in another moment in time the charge goes in the same circle but faster, where Δv is the difference in speed. i want to find the change in the magnetic dipole moment Δm.if magnetic dipole moment m=IA (assuming uniform I), how do you go from

$$m=IA ...to... Δm=\frac{1}{2}qΔvr ?$$Thanks in advance

 

[rude man]

well, what's the current as a function of speed v?

 

[iScience]

I(v)=$\lambda$v

 

[rude man]

I(v)=$\lambda$v

The problem says "a charge" so I would assume a single charge q rather than a charge distribution λ, so say the charge goes around N times/s, which is 2πRN m in 1 s, which says velocity v = 2πRN, which says the current is how much?

 

[iScience]

oh... got it now! thanks!

but another question: i can't say this for a single atom since current exists only on the outside, but for the case of a solid, wouldn't "IA" be more of a flux than a moment? and even for the case of a single atom, i thought moments were supposed to be some quantity times a distance, not an area.

 

[rude man]

oh... got it now! thanks!

but another question: i can't say this for a single atom since current exists only on the outside, but for the case of a solid, wouldn't "IA" be more of a flux than a moment? and even for the case of a single atom, i thought moments were supposed to be some quantity times a distance, not an area.

Not sure I know what you mean by invoking atoms and solids, but the main point of the magnetic moment μ = IA is that, in a B field, there is a moment (torque) τ applied to the coil or whatever medium carrying the current such that τ = μ x B.

You can easily show the validity of this formula by considering the torques on a rectangle of wire, sides 2a and 2b, carrying current I in a field B parallel to any side. For other shapes, integration would be necessary.

Magnetic moments are especially handy in describing permanent magnets. A p.m. with mag. moment μ will see a torque as per the above. So μ can be measured by pointng the p.m. at right angles to the B field and recording the torque. The A vector points from the S to the N pole. I offhand don't know another way to quantify permanent magnets.


Take a look at http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magmom.html

and

http://en.wikipedia.org/wiki/Magnetic_moment