In physics, Gauss’s law is a law that relates the distribution of electric charges and the electric field produced by them. According to this rule, the rendering of this rule was done by Carl Friedrich Gauss in 1835, but could not publish it until 1837. This law is one of Maxwell’s four equations. Gauss’s law can be derived from Coulomb’s law. (The opposite is also true – Coulomb’s law can be derived from Gauss’s law.) So let’s know about Gauss Ka Niyam.

## Gauss’s law

According to this law, the total electric flux in an imaginary closed surface is equal to the algebraic sum of all the charges in that closed surface. The surface integral of the normal component of the instruction electric field E about a point charge q is:

**E.dS = q/ε0**

It is known from this formula that the flux of the electric field produced by the surface has a net value of q/ε0 where q is the closed charge inside the surface. If there is no charge inside this surface then the electric field emitted from the surface will be zero i.e. (E=0) then,

**E.dS =0**

## Gauss’s Law in Differential Form

Consider a density distribution in which the charge density is The charge absorbed by a closed surface is represented by the volume integral of the instruction charge density of the closed volume by the surface, i.e. it has a value of dv. The equation is a differential equation of Gauss’s law, which means that the divergence of the electric field at a point is 1/ε0 of the volume density of the charge at that point. This is Maxwell’s divergence equation for the electric field.

## Applications of Gauss’s Law

By this rule the following can be found-

- electric field due to point charge
- electric field of a charged bullet shell
- electric field outside the bullet shell
- electric field inside the bullets shell
- bullet uniform charge distribution
- outside point charge distribution
- on the surface of the point charge distribution
- inside point charge distribution
- Electric field due to infinite line charge
- Electric field due to infinite cylindrical symmetrical charge
- Electric field due to an infinitely long flat seat of a bad conductor of charge
- Electric field due to concentric spherical shell

## Applications of Gauss’s Theorem

Gauss’s theorem can be used to find the electric field intensity at a point due to a given charge distribution. For this, we first imagine a surface which is symmetric about the given charge distribution and the point at which we have to calculate the electric field intensity is located on that surface. This surface is called a Gaussian surface. Then calculate the electric flux passing through this surface according to Gauss’s theorem.

## Important facts of Gauss’s law

Important facts of Gauss Ka Niyam are given below-

- Gauss’s theorem is based on the fact that the electric field intensity due to a point charge is inversely proportional to the square of the distance.
- Gauss’s theorem is mainly used to find the electric field intensity due to symmetric charge distribution.
- The Gaussian surface should be taken in such a way that there is no charge on it. According to Gauss’s theorem, the total number of electric field lines emanating from a point money charge q is q/ε₀.
- Gauss’s theorem also applies to the gravitational field.

## MCQs

**Question 1. The electric field intensity due to a uniformly charged solid dielectric sphere is maximum**

(a) at the center

(b) at any point midway from the center to the surface

(c) on the surface

(d) at infinity

Answer: (c) on the surface

**Question 2. A charge of 1 μC is placed at the center of a cube of side 0.2 m. The value of electric flux through each face of the cube in V/m will be**

(a) 1.12 × 104

(b) 2.2 × 104

(c) 1.88 × 104

(d) 3.14 × 104

(a) 1.12 × 104

(b) 2.2 × 104

(c) 1.88 × 104

(d) 3.14 × 104

Answer (c) 1.88 × 104

**Question 3. When a soap bubble is negatively charged, its Radius**

(a) decreases.

(b) increases.

(c) remains unchanged.

(d) The information is incomplete so cannot say anything.

(a) decreases.

(b) increases.

(c) remains unchanged.

(d) The information is incomplete so cannot say anything.

Answer: (b) increases.

**Question 4. The radii of two conducting spheres are a and b. On charging them with the same surface charge q, the ratio of the electric field intensities on their surface will be**

(a) 52 : a2

(b) 1 : 1

(c) a2 : 52

(d) b : 4

(a) 52 : a2

(b) 1 : 1

(c) a2 : 52

(d) b : 4

Answer: (b) 1 : 1

**Question 5. A charge is placed in a sphere and the electric flux emerging from it is q/ E n. How much will the value of the electric flux change if the radius of the sphere is halved?**

(a) will become 4 times already

(b) will become one fourth from earlier.

(c) will be halved already

(d) will remain unchanged.

(a) will become 4 times already

(b) will become one fourth from earlier.

(c) will be halved already

(d) will remain unchanged.

Answer: (d) will remain unchanged.

**Question 6. The value of the total electric flux coming out of the unit positive charge in air is**

(a) 0

(b) 0-1

(c) (4πε0)-1

(d) 4πε0

(a) 0

(b) 0-1

(c) (4πε0)-1

(d) 4πε0

Answer: (b) 0-1

## FAQs

**Write Gauss’s law?**

According to this law, the total electric flux in an imaginary closed surface is equal to the algebraic sum of all the charges in that closed surface.

**What is Gauss’s law related to?**

Gauss’s law is related to physics and electromagnetism.

**What is Gauss ka niyam inspired by?**

Gauss ka niyam is inspired by Carl Friedrich Gauss.

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