An electric dipole consists of 1.0 g spheres charged to ±2.0...

An electric dipole consists of $1.0 \mathrm{g}$ spheres charged to $\pm 2.0 \mathrm{nC}$ at the ends of a $10-\mathrm{cm}-10 \mathrm{ng}$ massless rod. The dipole rotates on a frictionless pivot at its center. The dipole is held perpendicular to a uniform electric field with field strength $1000 \mathrm{V} / \mathrm{m},$ then released. What is the dipole's angular velocity at the instant it is aligned with the electric field?

An electric dipole consists of $1.0 \mathrm{g}$ spheres charged to $\pm 2.0 \mathrm{nC}$ at the ends of a $10-\mathrm{cm}-10 \mathrm{ng}$ massless rod. The dipole rotates on a frictionless pivot at its center. The dipole is held perpendicular to
a uniform electric field with field strength $1000 \mathrm{V} / \mathrm{m},$ then released. What is the dipole's angular velocity at the instant it is aligned with the electric field?

Key Concepts

Electric Dipole

An electric dipole consists of two equal and opposite charges separated by a distance, creating a dipole moment. This concept is central in electrostatics, as it explains how a pair of charges interacts with external electric fields and exhibits distinct behavior compared to isolated charges.

Torque on a Dipole

When placed in a uniform electric field, a dipole experiences a torque that tends to align its dipole moment with the field direction. This torque arises because the forces on the two oppositely charged ends act in opposite directions, producing a rotational effect that is crucial in analyzing the dynamics of dipoles in fields.

Rotational Dynamics

Rotational dynamics involves the study of how torques produce angular accelerations and rotations in bodies. This includes the application of Newton's laws to rotational motion, using concepts such as angular velocity, angular acceleration, and angular displacement, which are vital for analyzing rotating systems.

Moment of Inertia

The moment of inertia is a measure of an object's resistance to changes in its rotational motion about an axis. It depends on both the mass of the object and the distribution of that mass relative to the axis. In problems involving rotating bodies, calculating the moment of inertia is essential for determining angular acceleration and kinetic energy.

Conservation of Energy in Rotational Motion

In rotational systems, the principle of conservation of energy states that the total energy remains constant if there is no non-conservative work done. Specifically, changes in potential energy, such as those due to an external field acting on a dipole, are converted into rotational kinetic energy. This concept is fundamental in relating the work done by torques to the resulting angular velocity.

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