Equation #10: Gauss’ Law
Every charge produces an electric field around it. Coulomb’s law comes in handy when we have one or two charges. It gets really cumbersome to use Coulomb’s law for calculations involving a bunch of charges and quite impossible when we have a macroscopic charged object, like a rod or sphere etc.
Gauss’ law helps you out in such cases, provided you have some kind of symmetry in the charge distribution. Most commonly we deal with planar, cylindrical and spherical symmetries. If you have a charged symmetric object, you just have to imagine a surface enclosing it and depending on the charge enclosed (calculated by charge density per unit length, area or volume), you can calculate the electric flux.
The electric flux is a quantity which is somewhat abstract. Basically, it gives you the “net amount of electric field lines” exiting that imaginary surface. For example, if you don’t have any charge enclosed, the amount of electric field lines going in = the amount of field lines coming out, hence net flux is zero.
An interesting song that will help you remember Gauss’ Law:
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