# Electric dipole's maximum angular velocity

• superamazinPI
Equating them and solving for \omega gives (pE/I)sin\theta.In summary, we have an electric dipole with charges +q and -q separated by a distance D in an electric field \vec{E} pointing in the positive y direction. The dipole has a moment of inertia I about its center of mass and is released from an angle \theta, allowing it to rotate freely. To find the magnitude of its angular velocity when pointing along the y axis, we can use the equations for dipole moment, torque, potential energy, and kinetic energy. Solving for \omega, we get (pE/I)sin\theta.
superamazinPI

## Homework Statement

Consider an electric dipole located in a region with an electric field of magnitude $$\vec{E}$$ pointing in the positive y direction. The positive and negative ends of the dipole have charges +q and -q, respectively, and the two charges are a distance D apart. The dipole has moment of inertia I about its center of mass. The dipole is released from angle $$\theta$$, and it is allowed to rotate freely.

What is $$\omega_{max}$$, the magnitude of the dipole's angular velocity when it is pointing along the y axis?

## Homework Equations

dipole moment p= qd

$$\vec{\tau}$$=$$\vec{p}$$X$$\vec{E}$$

U= -$$\vec{p}$$ $$\cdot$$$$\vec{E}$$

## The Attempt at a Solution

I attempted to use energy, but I am not sure how to do it correctly - does potential energy equal kinetic? is the potential energy the one described in the above equation?

dipole in a E field gives torque, torque is a force and can then be related to moment of inertia and angular acceleration

You can use your expression for U and (1/2)I\omega^2 for the KE.

## 1. What is an electric dipole's maximum angular velocity?

An electric dipole's maximum angular velocity is the highest rotational speed that a dipole can reach while being subjected to an electric field. It is a measure of how quickly the dipole is rotating around its center.

## 2. How is maximum angular velocity related to electric dipole moment?

The maximum angular velocity of an electric dipole is directly proportional to its electric dipole moment. This means that the larger the dipole moment, the faster the dipole can rotate under the influence of an electric field.

## 3. Can an electric dipole's maximum angular velocity be negative?

No, an electric dipole's maximum angular velocity cannot be negative. Angular velocity is a scalar quantity and is always positive. However, the direction of rotation can be either clockwise or counterclockwise.

## 4. What factors affect an electric dipole's maximum angular velocity?

The maximum angular velocity of an electric dipole is affected by the strength of the electric field, the distance between the charges in the dipole, and the mass and moment of inertia of the dipole.

## 5. How is maximum angular velocity calculated for an electric dipole?

The maximum angular velocity of an electric dipole can be calculated using the formula: ω = qE/I, where q is the charge of the dipole, E is the electric field strength, and I is the moment of inertia of the dipole.

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