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Introduction
Gauss’s law, one of two statements describing electric and magnetic fluxes. Gauss’s law for electricity states that the electric flow through any enclosed surface is proportional to the net electric charge enclosed by the surface. The law implies that there are isolated electric charges and that like charges repel each other whereas, unlike charges, they attract each other. Gauss’s law for magnetism states that the magnetic flux through any closed surface is zero; this law is consistent with the observation that isolated magnetic poles (monopoles) do not exist.
What is Gauss’s Law
According to Gauss’s law the electric flux through a closed surface is equal to the net charge
enclosed within the surface divided by vacuum’s permittivity.
According to Gauss’ law, the net flux of an electric field inside a closed surface is precisely proportional to the electric charge enclosed . It’s one of Maxwell’s electromagnetic laws’ four equations.A
Carl Friedrich Gauss first proposed Gauss’s Law in 1835, and it relates to the electric fields at points on a closed surface, as well as the net enclosed charge by that surface.
The electric field travelling through a specific area multiplied by the area of the surface in a plane perpendicular to the field is known as electric flux. The net flow of a given electric field across a given surface area divided by the charge enclosed must be equal to a constant, according to another version of Gauss’s law.
A positive electric charge produces a positive electric field. The law was first published in 1867 as part of a collection of works by Carl Friedrich Gauss, a notable German mathematician.
Gauss’s Law Equation
Let’s try to understand the concept of Gauss’s Law using integral equation
EdA=10Q —(1)
Where, E = electric field vector, Q = electric charge,0 = electric permittivity of free space A = outward pointing normal area vector
Since, flux is the strength of field passing through the surface
—-( 2)
Electric field can be understood as the flux density. Gauss’s Law implies that the total electrical flux through any surface that is closed is zero, unless the volume bounded by the surface contains a net charge.
Gauss Theorem
We know that there is always a static electric field around a positive or negative electric charge and within that static electric field there is a flow of flux. In reality this flux is radiated/emanated by the electric charge. Now, the amount of this stream of flux depends on the amount of charge it emanates from.
To discover this relationship, Gauss’s theorem was introduced. This theorem can be considered to be one of the most powerful and useful in the field of electrical science. We can find out the amount of flux radiated through the surface surrounding the charge by this theorem.
Gauss’s theorem states that the flow of electric flux through any closed surface surrounding a charge is equal to the net positive charge enclosed by that surface. Suppose the charges Q1, Q2_ _ _ _Qi, _ _ _ Qn are surrounded by a surface, then the theorem can be expressed mathematically by the surface integral as
Application of Gauss’s Law
- Electric Field due to an infinite charge plane sheet
Suppose an infinite charge plane sheet that has a surface charge density of σ. Let P be any point which is at r distance from sheet and E denote the electric field at point P. Assume a Gaussian surface in the shape of a cylinder with cross sectional area A and length 2r perpendicular to the charge sheet.
Electric field is at right angles to the end caps and is away from the plane (due to symmetry). It has the same magnitude at P and at the other cap at P’.
As a result, the total flux across the closed surface is
If is the charge per unit area in the plane sheet, then q = A is the net positive charge within the Gaussian surface.
Applying Gauss’s law,
- Electrostatic Shield
It is the method of isolating a specific region of space from the surrounding field. It works on the assumption that the electric field within a conductor is zero.
It is safer to sit inside a bus than on the open ground or under a tree during a thunder and lightning storm. The electric field inside the bus is zero, as the bus’s metal body offers electrostatic shielding. During a lightning strike, an electric discharge goes through the bus’s body.
Conclusion
The Gauss’s law is applied to the closed surface and it has various applications such as electric field due to infinite sheet and electrostatic shield. However in this article you will also get to know what Gauss’s law is and what is Gauss’s theorem? According to gauss’s law the electric flux through any closed surface equals zero. Hope this article is useful for you and will help you with your academics.
