## Even a Stationary Charge Has a Magnetic Field

A stationary charge has a magnetic field. This statement may seem to be a contradiction to what you have already learned about magnetic fields. Only moving charges produce magnetic fields, right? Let me explain.

Imagine yourself sitting in a wagon rolling along at a steady, constant speed. You have a charge in front of you. You measure it and it has an electric field but no magnetic field. You say I am wrong. But then you jump off the wagon, and you are on the ground. The charge is now moving relative to you. You measure again and you find that it has both an electric and a magnetic field. Let's say your friend Joe was standing by the side the whole time and your friend Bill stays in the wagon the whole time. For them nothing about the charge or its fields changed. Joe always observes the magnetic field, and Bill never observes it. When you were in the wagon you didn't observe the magnetic field, and then later you did. But nothing ever changed about the charge. The act of you jumping off the wagon didn't cause the charge to create a magnetic field. The act of you jumping off did not change anything about the charge, as witnessed by your two friends. The only way to reconcile this dilemna is to admit that the charge always had the magnetic field. You just couldn't observe it from your original perspective. The electric and magnetic fields are really different aspects of a single electromagnetic field. Here's an analogy. A three-dimensional cylinder looks like a two-dimensional circle from the end perspective and it looks like a two-dimensional rectangle from the side perspective. Only from other perspectives can you see the true three-dimensional nature. Similarly, when you are observing a charge from a perspective that is at rest with respect to the charge, the magnetic field is hidden.

Just as space and time are equal partners in the web of 4D space-time, the electric and magnetic field are equal partners in the 4D electromagnetic field. The voltage is analogous to time (1D), and the magnetic vector potential to space (3D). Now you understand why Maxwell's equations are correct in terms of special relativity. This fable of the charge and the wagon also explains why charges moving at constant velocity do not radiate. If they did, you could cause the charge to radiate by jumping off the wagon, but then your two friends would make contradicting observations. Relativity works behind the scenes of many electromagnetic phenomena.

## Solar Panel Basics

Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.

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