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## Homework Statement

A long hollow nonconducting cylinder (radius R= 0.060 m, length L= 0.70 m) carries a uniform charge per unit area of σ= 4.0 C/m^2 on its surface. Beginning from rest, an externally applied torque causes the cylinder to rotate at constant acceleration α= 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 ω= 200 rad/s.

(Answer 4.6μW)

## Homework Equations

I=S[itex]_{avg}[/itex]=[itex]\frac{1}{cμ_{0}}[/itex] * [(E[itex]_{max}[/itex])[itex]^{2}[/itex]*sin[itex]^{2}[/itex](kx-ωt)]

## The Attempt at a Solution

The intensity I of the electromagnetic wave is [itex]\frac{Power}{Area}[/itex] where I assumed the area would be the surface area of the cylinder (2[itex]\pi[/itex]*r*L).

so to find the net power through the cylinder I thought it would just be I*area.

From a previous chapter, I determined that E=[itex]\frac{σ}{2ε_{0}}[/itex].

With angular acceleration α=40rad/s^2 the cylinder would reach the angular velocity

ω= 200rad/s^2 in t=5 seconds.

I'm not sure if this is the right approach to the problem. I don't know what to do about x or the angular wave number k in the intensity function.