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Homework Statement
A light bulb with resistance R is attached on a metal rod which is rotating around the point O on the figure. The metal rod is in contact with an electrical conductor which is a part of a circle with radius d. The metal rod and the circular electrical conductor is a closed circuit. The rod now rotates with angular velocity [itex]\omega[/itex] through the constant magnetic field pointing out from the paper.
a)
Find an expression for the induced current through the light bulb, expressed in terms of [itex]\omega[/itex], d, B and R.
Homework Equations
IR=vBr
where v is the tangential speed of the rod perpendicular to the Bfield (every speed is perpendicular to the Bfield, since we are looking at a plane) and r is the length of the rod moving at this speed.
I=[itex]\frac{\omega Br^{2}}{R}[/itex]
v substituted for [itex]\omega r[/itex]
The Attempt at a Solution
Since the every part of the rod is moving with different linear speeds, we should integrate the RHS from the 0 to d with respect to r and that should be it right?
i get:
I=[itex]\int^{d}_{0}\frac{\omega Br^{2}}{R}[/itex]
I=[itex]\frac{d^{3}B\omega}{3R}[/itex]
But when i look up the solution it says:
I=[itex]\frac{Bd^{2}\omega}{2R}[/itex]
so who's right?
Edit: Problem solved!
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