# Homework Help: Current loop rotating to give magnetic moment

1. Nov 7, 2012

### nautola

1. The problem statement, all variables and given/known data
A uniform non-conducting ring of radius
0.816 cm and total charge 6.76 µC rotates
with a constant angular speed of 1.73 rad/s
around an axis perpendicular to the plane of
the ring that passes through its center.
What is the magnitude of the magnetic
moment of the rotating ring?

r = .00816 m
q = 6.76E-6 C

2. Relevant equations
μ = IA
I = dq/dt
A = $\pi$r^2

3. The attempt at a solution
I took the current and said it was equal to qω/2∏, since that gives charge/time. Then I multiplied by area. When that didn't work I decided to take the same approach but integrating from 0 to ∏/2 with r replaced with (rcosθ), to be the radius of any point on the loop, making a circle as a function of angle. Then I said charge was equal to λr dθ, since the charge is uniform. I took that function and integrated it: λω(r^2)/2∫(cosθ)^2 dθ, 0,∏/2. Then I multiplied by 4, for each of the quarters of the loop.
The idea is that each infinitesimally small point on the loop has a charge and will behave like a charge orbiting and integrating over all of the possible radii gives the combined magnetic moment. However, this didn't work and I lost points. I don't understand why.

2. Nov 7, 2012

### Delphi51

qω/2∏ * area should be correct. Did you get 3.89 E-10 ?

3. Nov 7, 2012

### nautola

I had almost that...but not quite within 1%. Which is what our online homework requires. So my approach was correct, just not some value.
Thanks.