Hello students in this session we will learn about Gauss’s law in electrostatics and also learn some important points about it. So lets start…

## Gauss’s law

According to Gauss’s law, the total electric flux passing through any closed surface is equal to the net charge **q** enclosed by it divided by **ε _{0}**.

**ϕ = q/ε _{0}**

Here the term q on the right side of Gauss’s law includes the sum of all charges enclosed by surface. The

charges may be located anywhere inside the surface.

## Proof of Gauss’s Law:

## Important points about Gauss’s law:

(i) Gauss’s law is true for any closed surface, no matter what its shape or size.

(ii) In the situation, when the surface is so taken that there are some charges inside and some outside, the electric field (whose flux appears on the left side of Gauss’s law) is due to all the charges, both inside and outside the surface. However, the term q on the right side of Gauss’s law represents only the total charge inside the surface.

(iii) The surface that we choose for the application of Gauss’s law is called the Gaussian surface. You may

choose any Gaussian surface and apply Gauss’s law. However, do not let the Gaussian surface pass through any discrete charge, because electric field is not well defined at the location of discrete charge.

However, the Gaussian surface can pass through a continuous charge distribution.

(iv) Gauss’s law is often useful for a much easier calculation of the electric field, when the system has some symmetry. This is achieved by the choice of a suitable Gaussian surface.

(v) In a closed surface incoming flux is taken negative while outgoing flux is taken positive. If a closed body (not enclosing any charge) is placed in an electric field (either uniform or non–uniform) total flux linked with it will be zero.

(vi) In a Gaussian surface electric flux **ϕ** = 0 does not imply E = 0 but E = 0 implies electric flux **ϕ** = 0.

(vii) If the net flux is positive, then net positive charge is enclosed. If the net flux is negative, then net negative charge is enclosed in the closed surface.

(viii) If the closed gaussian surface have n symmetrical faces then the electric flux passing through one face will be 1/n times the total flux passing through the surface.

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**✅Sharpen Your Pencil ✍️**

**Q. 1. Positive electric flux indicates that electric lines of force are directed**

(a) outwards (b) inwards

(c) either (a) or (b) (d) None of these

**🔻Comment the Answer💬**

**Q. 2. In the figure below, a configuration of four closed surfaces and three charges of -2Q, + Q, and –Q is shown. What is the electric flux passing through each surface?**

**🔻Comment the Answer💬**

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