Question

The potential energies associated with four orientations of an electric dipole in an electric field are `(1) -5 U_0, (2) -7 U_0, (3) 3 U_0, and (4) 5 U_0`, where `U_0` is positive. Rank the orientationa according to the
a. angle between the electric dipole moment `vec P` and the electric field `vec E, and
B magnitude of the torque on the electric dipole, greatest first.

Answer 1

a. `U = -p E cos theta = p E cos (180 - theta)`
The more is U, the more is `theta`. So ` angle4 gt angle 3 gt angle 1 gt angle2`.
b. If angle between p and E is more closer to `90^(@)`, then torque is more. If angle is closer to `0^(@)` or `180^(@)`, then torque is les. It means the lesser is the magnitude of potential energy, the more is toque and vice versa. So `3 gt 1 = 4 gt 2`.