Flux and Gauss's Law

For a given charge distribution, the electric field can be calculated using Coulomb's Law. There are two possible methods: Calculate the field vectors due to all the charges and then add them vectorially, or first calculate the electric potential V due to these charges and take its negative gradient.

For more information on this subject, see the Electric Potential module.
There exists an alternate method to finding the electric field, which is provided by Gauss's Law. This "new" method is much more elegant and powerful when there is a certain symmetry to the physical situation--for example, when a charge distribution is spherically symmetric.

Suppose we construct a closed surface around parts of a given charge distribution. This enclosed surface, called a Gaussian Surface, can be of any shape and size we decide. (Note that a Gaussian surface is not a physical surface, such as a plastic bag, but is a mathematical construct.)

Gauss's Law relates the electric fields on the Gaussian surface to the net charge inside it.

For instance, take the above illustration. The electric field (shown by the vectors is proportional to the enclosed charges only. Therefore, only charges q2, q3, and q5 affect the net electric field through the Gaussian surface. The other charges have no effect!

Before we can formulate the exact statement of Gauss's Law, we need to introduce and discuss the concept of flux in a general way. Flux plays an important role not only in electrostatics, but also in areas such as fluid mechanics.

FLUX

The word flux is associated with something flowing. This "something" may be the water flow in a river or the mass flow in lava. Similarly, we can introduce "electric flux," visualizing the electric field vector "flowing" through a surface area.

Since it is easiest to visualize the water flowing, we will use the water flow as the prototype example in the discussion of flux.

Go on and try one such example now.


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