Exercise. An electric dipole located in a uniform electric field is allowed to r

Question

Exercise. An electric dipole located in a uniform electric field is allowed to rotate on a frictionless pivot point (Center point between charges in the diagram). Initially the dipole is oriented perpendicular to the electric field, but of course it will respond to the electric forces on the point charges by rotating to align parallel to the electric field. Derive a mathematical expression for the angular velocity at the instant in time that the dipole first aligns with the electric field. You must begin your calculation from conservation of energy! HINT:You can significantly reduce your effort if you review how potential energy is related to the electric dipole moment.
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Explanation / Answer

The potential energy U of a dipole with dipole moment p in an electric field E is

U = -p•E

which is at its maximum of 0 when the field is perpendicular to the dipole. When the dipole is parallel to the field, the potential energy has decreased to its minimum of -pE so the kinetic energy must be pE.

Using rotational kinematics,

T = ½I2 = pE and solving for ,

= (2pE/I)½

It is not possible to be more specific without details about the actual rotational inertia I, which would require information about the masses and separation of the dipole components.

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