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Need help setting up Eqtn of motion.

  • Thread starter robousy
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Torque in Electric Field...need help with eqtns of motion...

Ok - I have a charged square plate Q with a weightless rod attached through the centre of the plane so that the plate can rotate like a propeller.

Half of the plate sits in an E field and so feels a torque.
The E field drops off as [tex] \frac{1}{r^2} [/tex]

I need to set up the equation of motion.

Now, I know that:

[tex] \Gamma = Fd [/tex]

My problem is that [tex]F=F(\theta) \:and\: d=d(\theta) [/tex]

i.e as the plate rotates less of it will feel the electric field - it will be completely half immersed in the E field at an angle of 0 deg (perp to field)and will feel the max force, and be at a min when the plate is parallel to the field and feel zero force.

Also as the plate rotates some if it will be closer to the E field and some of it will be further away so there is also the theta dependant distance.

Can anyone help me set up the eqtns of motion?
 
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