Electric Dipoles: Introduction

The electric dipole is on of the most fundamental sources of light in the universe. At its heart, a dipole is composed of two charges of opposite sign separated by some distance d.

The figure above here is the general diagram for the calculations that follow. We have two charges: positive (red) and negative (blue) separated by a distance d along the x-axis. Our task will be to find the electric field at a point P situated somewhere far away from the dipole. The vectors $\overset{\rightharpoonup }{r}_1,\overset{\rightharpoonup }{r}_2, \text{and} \overset{\rightharpoonup }{R}$ point from the negative charge, positive charge, and origin, to the point P, respectively.

The outline of this section and the next is as follows:

1. We will review oscillating charges and how they produce traveling EM waves
2. The present section derives the electric field for a STATIC dipole
3. An advanced section derives the electric field for an oscillating dipole

At this point, it is worth noting that when Einstein formulated general relativity, he did so in a manner that was consistent with Maxwell's equations. Relativity is a generalization of mechanics, it did not directly modify electromagnetism. That means that the calculations to follow are consistent with relativistic effects.

Before moving on, let's review oscillating charges in the form of an interactive simulation. Navigate to THIS Links to an external site. interactive simulation. This will not be a graded assignment but I want you to perform the following actions and consider the questions:

1. Notice the electric field line pattern and how it relates to our previous discussions.
2. Next, click the 'oscillation' check box to turn off the oscillations
3. Grab the charge and wiggle it gently in the horizontal direction. Note the pattern of the field lines and which direction the waves travel.

This is the essence of how light is made in the universe and it is critical that you internalize this process.