1. Gauss’s theorem
2. Gauss’s theorem states that electric flux over a closed surface is \(\frac{1}{\varepsilon_0}\) times the total charge enclosed by the surface.
Gauss’s theorem may be expressed as
\(\int\overrightarrow E.d\overrightarrow s\) = \(\frac{1}{\varepsilon_0}q\)
3. Gauss’S Law:
Gauss’s theorem states that the total electric flux over a closed surface is \(\frac{1}{\varepsilon_0}\) times the total charge enclosed by the surface. Gauss’s theorem may be expressed
\(\int\overrightarrow E.d\overrightarrow s\) = \(\frac{1}{\varepsilon_0}q\) or \(\phi=\frac{1}{\varepsilon_0}q\)
Proof:
Consider a charge +q .which is kept inside a sphere of radius ‘r’.
The flux at ‘P’ can be written as,
\(\phi=\int \overrightarrow E.d\overrightarrow s\)
But electric field at P, E =
P,E = \(\frac{1}{4\pi \varepsilon_0}\frac{1}{r^2}\)
∴ \(\overrightarrow E.d\overrightarrow s\) \(\frac{1}{4\pi\varepsilon_0} \frac{1}{r^2}ds\)
Integrating on both sides we get,
Important points regarding Gauss’s law:
- Gauss’s law is true for any closed surface.
- Total charge enclosed by the surface must be added (algebraically). The charge may be located anywhere inside the surface.
- The surface that we choose for the application of Gauss’s law is called the Gaussian surface.
- Gauss’s law is used to find electric field due to system of charges having some symmetry.
4. \(\int \overrightarrow E.d\overrightarrow s\) = \(\frac {q_{enclosed}}{\varepsilon_0}=\frac{q}{\varepsilon_0}\)
\(q =\varepsilon_0\int\overrightarrow E.d \overrightarrow s C\)
