# Dipole as a torsion pendulum

1. Jan 30, 2008

### pianoman2700

An electric dipole p is suspended as a torsion pendulum, which is allowed to pivot
about the nz-axis only. The dipole has moment of inertia I and the torsion spring
has Hooke constant K. In the absence of an electric Field the torsion pendulum's
equilibrium orientation theta-not is equal to zero. The dipole's orientation is allowed to change only in the direction permitted by the torsion pendulum (i.e., rotation 
about the nz axis). A uniform electric Field E is applied.

(a) Derive the equations of motion for the torsion pendulum for arbitrary dipole
moment p and uniform electric Field E.

(b) Find, from the equations of motion, the equilibrium orientation of the pendulum
Theta-not(E) when the uniform electric field is E

I'm not really even sure where to start with this problem. I know the equations:
torque = p x E (for a dipole)
torque = K*theta (for a torsion pendulum)
torque = I*alpha (for rotation)

Other than that, though, I don't know where to go. Am I supposed to solve for theta and derive the rest of the equations from there, or should I solve for alpha and integrate? Or am I on the wrong track completely?

Any help would be much appreciated.