Posted by sand on .
A long hollow nonconducting cylinder of radius 0.060 m and length 0.70 m carries a uniform charge per unit area of 4.0 C/m^2 on its surface. Beginning from rest, an externally applied torque causes the cylinder to rotate at constant acceleration of 40 rad/s^2 about the cylinder axis. Find the net power entering the interior volume of the cylinder from the surrounding electromagnetic fields at the instant the angular velocity reaches 200 rad/s.

physics 
drwls,
You need to use the equation for the power radiated by accelerating charge. This requires fairly advanced E&M "retarded potential" theory.
The total charge on the cylinder surface is
Q = 2*pi*R*L*(4.0 C/m^2) = 1.056 C
The charge accelerates at a rate
a = R*w^2 = 2400 m/s^2
The radiated power (into the cylinder, to keep it accelerating) is
P = (2/3)*k Q^2*a^2/c^3,
where k is the Coulomb constant, 8.99*10^9 N/m^2/C^2 and c is the speed of light.
(Ref.: Reitz and Milford, Foundations of Electromagnetic Theory)
This is a nonrelativistic formula, requiring
w*R/c <<1
I get 1.4*10^9 Watts 
physics 
sand,
But the answer is 4.6 micro watts
Anyhow thanks for your time 
physics 
drwls,
The surface charge has both centripetal and tangential acceleration, but the latter is negligible. I did not include it. I cannot explain the large discrepancy. See what you get using the formula for radiation by accelerating charge.