Q. 77

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Found in: Page 713

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# An electric dipole consists of spheres charged to at the ends of a -long 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 , then released. What is the dipole’s angular velocity at the instant it is aligned with the electric field?

The dipole’s angular velocity is.

See the step by step solution

## Step 1: Given Information

We have given a dipole consists of spheres, charge, length of massless rodand a uniform electric field with field strength.

## Step 2: Law of conservation of energy

By the law of conservation of energy, the entire energy that the dipole has at the moment it is aligned perpendicular to the electric field will be converted to kinetic energy, which in this case is rotational. Consider the formula for the energy of a rotating system

,

Where is the moment of inertia. For our case, the moment of inertia will be

,

This is because the moments come from the two spheres, each of which connected by a massless rod, keeping them at distance from the axis of rotation. Found that the kinetic energy is

Therefore, we can express the angular velocity as

## Step 3: Explanation

Now, as we mentioned in the introduction, finding the kinetic energy in terms of the electric potential energy.

Where is the magnitude of the dipole moment and is the magnitude of the electric field.

Let us disregard the minus sign for simplicity, and have

.

Substituting this result in our result for the angular velocity we will have

As the expression can't be simplified further. We can now calculate and have