This lesson describes the superposition theorem, an important concept in physics in general. Here, we will apply the theorem to electricity in general and point out some important applications.
Superposition Theorem Definition
The superposition principle applies to many areas of physics, but basically, it's a way to combine the electric fields of many charges together to make up a more complicated electric field. It is a great theorem because it makes things simpler instead of more complicated. How often does that happen! You can see the superposition principle in action when you watch multiple rain drops in a lake, or listen to multiple voices in a room.
In the case of rain on a lake, the ripples all go through each other; you can see many separate, circular ripples in the pond. Likewise, all the voices of people talking in a room can be heard at the same time. You can usually pay attention to only one, but any person you listen to will come through clearly. The sound waves do not run into each other. The superposition principle also applies to things we can't see, like electric fields.
Anything with an electric charge creates an electric field. An electric field is invisible, but applies force to anything else with an electric charge. You can think of it like there are many little notecards hanging in space, saying 'a charge q will experience a force qE at this point.' Remember, the electric field E is a vector and has both magnitude and direction. The electric field due to a charge q is easy to calculate, it is E = qr / (4 * pi * epsilon_0 * r^3) where epsilon_0 is a constant and r is the vector between the field point and the charge.
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Now the problem that the superposition solves is how one calculates the electric field due to many charges. If we go back to our little notecards hanging in space, we now have two notecards, one saying 'I will apply force qE1 to a charge q' and one saying 'I will apply force qE2 to a charge q.' The superposition principle quite simply says that the two electric fields do not interfere with each other, that the total electric field at that point is just the sum of the electric fields due to two different charges. In other words, we can replace the two notecards with one notecard that says 'I will apply force qE3 = E1 + E2 to a charge q.'
Other Superposition Theorem Examples
The principle also applies to electric signals like those that run through telephone lines and computer cables; and electromagnetic waves like visible light, radio waves, and microwaves. There are many things that can absorb electrical signals, like a ground wire, and many things that can reflect or absorb electromagnetic waves, like radio waves getting weaker when you're under a concrete bridge or tunnel, but the signals and waves do not bounce off or get absorbed by each other. This means that radio towers can all transmit at the same time without worrying that other towers will interfere with them, just as long as they transmit at different frequencies, because if they did you would hear the sum of two radio stations.
So, to sum up, the superposition principle is a way to combine the electric fields of many charges together to make up a more complicated electric field. Put another way, electric fields, which are invisible fields that apply force to anything else with an electric charge, do not interfere with each other, they simply add together. There can literally be any number of fields added together. Lastly, remember that the electric field at any point is a vector, and you must add the two fields as vectors.
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