Dipole in an Uniform Electric Field:

[fallen186]

Dipole in an Uniform Electric Field:
torque is calculated about the position of either charge has the magnitude FLsin(x) = qELsin(x) = pEsin(x). The direction of the torque vector is into the paper such that it tends to rotate the dipole moment vector p so it aligns with the direction of E. The torque can be expressed most concisely as the cross product: T = p x E

I don't know why the magnitude is F * L sin(x) or why qE turns into pE. And I don't understand what the concept iit s trying to tell me. It would also be helpful if someone could explain the hand thing for torque. I understand most of the stuff about torque but not the hand thing.

x = theta
L = distance between charges in dipole
p = vector of the dipole movement that points from negtive charge to positive.
p =q*L

 

[Born2bwire]

The dipole moment is defined as being L*q, so qELsin(x) = pEsin(x) by definition. As for F*L*sin(x), that's simply the scalar form of the vector cross product of F x L. Torque is defined as the cross product between the force vector and the vector denoting the lever arm. To find the torque on a dipole, they fix one of the charges as the center of rotation (or choose the midpoint, the result is the same since the magnitude of the force is the same) and assume that the length between the charges (or the dipole moment) to be the lever arm. The force is the Lorentz force resulting from the electric field.

I think you should brush up on torque and vectors because these are very basic concepts.