Calculation of Electric Field at a Distance 3d from a Dipole

When considering the electric field at a distance 3d from a dipole, we can assume that the separation between the charges forming the dipole is negligible compared to this distance. This assumption allows us to simplify the calculation and consider the dipole as a point charge.

1. Electric Field at the Midpoint of the Dipole (Distance d)

At the midpoint of the dipole, the electric field due to the positive charge and the electric field due to the negative charge cancel each other out. Thus, the net electric field at this point is zero.

2. Electric Field at a Distance 3d from the Dipole

To calculate the electric field at a distance 3d from the dipole, we can consider the dipole as a point charge located at the midpoint between the positive and negative charges. The electric field due to a point charge is given by Coulomb's Law:

E = k * q / r^2

Where E is the electric field, k is the Coulomb's constant, q is the magnitude of the charge, and r is the distance from the charge.

In this case, the charge is the dipole moment, which is the product of the magnitude of the charge and the separation between the charges forming the dipole. Let's assume the dipole moment is represented by p.

Therefore, the electric field at a distance 3d from the dipole can be calculated as:

E = k * p / (3d)^2

Simplifying the equation:

E = k * p / 9d^2

Conclusion:

The magnitude of the electric field at a distance 3d from a dipole is given by the equation E = k * p / 9d^2, where k is the Coulomb's constant and p is the dipole moment. This equation assumes that the distance d is much greater than the separation between the charges forming the dipole.

So, the magnitude of the electric field at a distance 3d is one-ninth of the magnitude of the electric field at the midpoint of the dipole.