Electrostatics And Potential Energy

To find the electrostatic potential energy of the charge configuration, we can use the formula for the potential energy between two point charges:

where:

• is the electrostatic constant.
• and are the magnitudes of the charges.
• is the distance between the charges.

Given:

• The charges are placed at and , so the distance .

Now, calculate the electrostatic constant :

Substitute all the values into the formula for :

Calculate:

Thus, the electrostatic potential energy of the charge configuration is . Hence, the correct option is:

Answer:

To determine the electric field at a point equidistant from the centers of both dipoles and , we will calculate the electric fields due to each dipole and then find the resultant electric field.

The formula for the electric field due to a dipole at a point along the axial line is given by:

where is the dipole moment, is the distance from the center of the dipole to the point, and is the permittivity of free space.

For dipole :

For dipole :

The distance from each dipole to point is half the distance between them:

Calculate the electric field due to dipole :

Calculate the electric field due to dipole :

The electric fields and are perpendicular to each other. The resultant electric field is given by:

Therefore, the electric field at point is .