# Need help setting up Eqtn of motion.

1. Aug 15, 2005

### robousy

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 $$\frac{1}{r^2}$$

I need to set up the equation of motion.

Now, I know that:

$$\Gamma = Fd$$

My problem is that $$F=F(\theta) \:and\: d=d(\theta)$$

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?

Last edited: Aug 15, 2005