what intensities of electric field due to an dipole formed by charges -q and +q at points at a large distance r in end on position and broad on position

To understand the electric field intensities produced by an electric dipole at a distance, we need to consider two specific orientations: the end-on position and the broadside position. An electric dipole consists of two equal and opposite charges, -q and +q, separated by a distance, d. The dipole moment, denoted as p, is defined as p = qd. When we analyze the electric field at a point far away from the dipole, we can derive expressions for both configurations.

Electric Field in End-On Position

In the end-on position, the point of interest lies along the axis of the dipole, extending from the positive charge towards the negative charge. The electric field intensity (E) at a distance r from the dipole can be expressed as:

E_end-on = (1 / (4πε₀)) * (2p / r³)

Here, ε₀ is the permittivity of free space. This formula indicates that the electric field intensity decreases with the cube of the distance from the dipole. The factor of 2 arises because the contributions from both charges add constructively along the dipole axis.

Example Calculation

Suppose we have a dipole with a dipole moment of p = 1 × 10⁻⁹ C·m and we want to find the electric field at a distance of r = 1 m:

E_end-on = (1 / (4πε₀)) * (2 * 1 × 10⁻⁹ / (1)³)

Calculating this gives us:

E_end-on ≈ 1.4 × 10⁻⁹ N/C

Electric Field in Broadside Position

In the broadside position, the point of interest is located perpendicular to the axis of the dipole, equidistant from both charges. The electric field intensity in this configuration is given by:

E_broadside = (1 / (4πε₀)) * (p / r³)

In this case, the contributions from the two charges partially cancel each other out, resulting in a smaller electric field compared to the end-on position. The factor of 1 reflects this cancellation effect.

Example Calculation

Using the same dipole moment of p = 1 × 10⁻⁹ C·m and a distance of r = 1 m, we can calculate the electric field:

E_broadside = (1 / (4πε₀)) * (1 × 10⁻⁹ / (1)³)

This results in:

E_broadside ≈ 0.7 × 10⁻⁹ N/C

Comparative Analysis

From these calculations, it becomes evident that the electric field intensity in the end-on position is greater than that in the broadside position. This difference arises from the geometric arrangement of the charges and how their electric fields interact at a distance. The end-on position allows for a more direct alignment of the field lines, while the broadside position results in a more complex interaction that diminishes the overall field strength.

In summary, the electric field intensities due to a dipole at a large distance vary significantly based on the orientation of the observation point relative to the dipole. Understanding these concepts is crucial for applications in electrostatics and fields involving dipole interactions.