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The potential energies associated with f...

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 orientation according to the 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.

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To solve the problem, we need to analyze the potential energies associated with the orientations of the electric dipole in the electric field. The potential energy \( U \) of an electric dipole in an electric field is given by the formula: \[ U = -\vec{P} \cdot \vec{E} = -PE \cos \theta \] where: - \( \vec{P} \) is the electric dipole moment, ...
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