E4.2 Gauss's Theorem:

Gauss Law can be applied only to any closed surface. Sometimes, an imaginary closed surface

is necessary to be drawn around a charge which is called Gauss's Surface.

It gives a relation between the number of lines of force and the net charge $Q$ enclosed by the closed surface.

The total of the electric flux out of a closed surface is equal to the charge enclosed divided by the Permittivity. i.e. $\phi = \frac{Q}{\epsilon_0}$ 

Gauss's Law states that: "The total electric flux passing through a closed surface enclosing a charge is equal to $\frac{1}{\epsilon_0}$ times the magnitude of net charge enclosed by the closed surface."

Mathematically,

Electric flux ($\phi$) is the product of electric field strength ($E$) and the area ($A$) is

$\phi = E.A$ .......... (i)

Where, $E = \frac{Q}{4 \pi \epsilon_0 R^2}$ and $A = 4 \pi R^2$

Then, if a surface encloses a charge inside it, the electric flux passing through it is as follows,

$\phi = \frac{Q}{\epsilon_0}$ .......... (ii)

Where, $Q$ is the net charged and $\epsilon_0 = 8.85 * 10^{-12} F/m$ is the permittivity of Vacuum.

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