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# Waves: Of Special Interest to Physics C Students

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Practice problems for these concepts can be found at:

Waves Practice Problems for AP Physics B & C

### Maxwell's Equations

Okay, we'll get this out of the way right now: You will not have to solve Maxwell's equations on the AP Physics exam. These four equations include integrals the likes of which you will not be able to solve until well into college physics, if then. However, you can understand the basic point of each equation, and, most importantly, understand the equations' greatest consequence.

Maxwell obtained this wave speed as a mathematical result from the equations. He noticed that, when the experimentally determined constants were plugged in, the speed of his "electromagnetic waves" was identical to the speed of light.3 Maxwell's conclusion was that light must be an electromagnetic wave.

What are Maxwell's equations? We're not even going to write them out, for fear that you might throw down your book in trepidation. If you're really interested in the integral or differential form of the equations, you will find them in your physics book (or on a rather popular T-shirt). While we won't write the equations, we'll gladly summarize what they are and what they mean.

• Maxwell equation 1 is simply Gauss's law: The net electric flux through a closed surface is proportional to the charge enclosed by that surface.
• Maxwell equation 2 is sometimes called Gauss's law for magnetism: The net magnetic flux through a closed surface must always be zero. The consequence of this equation is that magnetic poles come in north/south pairs—you cannot have an isolated north magnetic pole.
• Maxwell equation 3 is simply Faraday's law: A changing magnetic flux through a loop of wire induces an EMF.
• Maxwell equation 4 is partly Ampére's law, but with an addition called "displacement current" that allows the equation to be valid in all situations. The principal consequence is that just as a changing magnetic field can produce an electric field, a changing electric field can likewise produce a magnetic field.

Practice problems for these concepts can be found at:

Waves Practice Problems for AP Physics B & C

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