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What Is Gauss Law (Class 12): Applications, Equations, Theorem

Aditya Jha

Updated on 17th July, 2023 , 5 min read

Gauss Law Class 12 Overview

According to Gauss' law, the total quantity of electricity flux produced by an enclosed surface equals the amount of charge maintained divided by the permittivity. Compounding the electrical field by the region of the plane-projected surface perpendicular to the field yields the electric flux in a particular area.

Similar Read: Brewster Law

What is Gauss Law Class 12?

In physics and electromagnetism Gauss' law, frequently referred to as "Gauss' flux thesis" (or sometimes referred to as "Gauss' theorem"), is a law that links the spatial distribution of electrical charges to the consequent electric field. It asserts in its integral form that the flux of the electric field out of any arbitrary closed surface is proportional to the electric charge enclosed by the surface, regardless of how the charge is distributed. 

Also Read About- Moseley Law & SI Unit of Resistance

Gauss Law Class 12 Highlights

The following table gives details about the Carl Friedrich Gauss-

Particulars

Details

Full Name

Johann Carl Friedrich Gauss

Date of Birth

30 April 1777

Place

Brunswick, Principality of Brunswick-Wolfenbüttel, Holy Roman Empire

Age

77 Years 

Died

23 February 1855

Göttingen, Kingdom of Hanover, German Confederation

Alma Mater

  • Collegium Carolinum
  • University of Göttingen
  • University of Helmstedt (Ph.D.)

Awards

Lalande Prize (1809)

Copley Medal (1838)

Fields 

Mathematics and Sciences

Institutions

University of Göttingen

Gauss Law Class 12 Inventor

Joseph-Louis Lagrange proposed the law in 1773, followed by Carl Friedrich Gauss in 1835, both in the context of the attraction of ellipsoids. The Gauss Law, as we know it now, was developed later, in 1867, by German mathematician and scientist Johann Carl Friedrich Gauss. Gauss, regarded as one of history's most famous mathematicians, had a significant impact on many disciplines of science and mathematics. Gauss devised novel and effective orbital determination methods. Carl Friedrich Gauss' mom had no idea when her son was born; she only knew that he was born on the third day of the week. Gauss later resolved his birthday conundrum by discovering methods for determining dates in the past and future.

Also read about- Difference between Interference and Diffraction

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What is the Gauss Law Class 12 Formula?

Gauss' law, often known as Gauss' flux theorem, states that the total flux of electricity going through every enclosed surface equates to the net electrical charge (q) contained by it divided by 0.

ϕ = q/ε0

Where,

Ï• = The flow of electricity across a closed surface S containing any volume V

Q = entire charge contained within V

ε0 = The electric constant

Gauss Law Class 12 Theorem

The Gauss Law, as we know it now, was developed later, in 1867, by German mathematician and scientist Johann Carl Friedrich Gauss. Gauss, regarded as one of history's most famous mathematicians, had a significant impact on many disciplines of science and mathematics. Gauss devised novel and effective orbital determination methods. Carl Friedrich Gauss' mom had no idea when her son was born; she only knew that he was born on the third day of the week. Gauss later resolved his birthday conundrum by discovering methods f The net flow over a surface that is closed is proportional to the net charge present in the volume spanned by the closed surface, based on the Gauss theorem. To put it another way, in electrostatics, the Gauss theorem correlates the "movement" of electric fields (flux) to charges within an enclosed surface. The net electrical flow is 0 if no electrical charges are contained on the surface. As a result, the number of electric field lines approaching the surface matches the number of electric field lines exiting it.or determining dates in the past and future.

Φ = → E.d → A = qnet/ε0

Applications for Gauss Law Class 12

Gauss' Law is suitable to tackle complex electromagnetic issues with unorthodox symmetry, such as a cylinder, spherical, or planar symmetry, as shown in the examples below. In other cases, calculating the field of electricity is difficult and requires a large amount of integration. The Gauss Law can be applied to the following-

  1. An electric field is created by an equally charged, infinite straight wire.
  2. An electric field is generated by an equally charged infinite plate sheet.
  3. An electric field is created by a thin, equally charged spherical shell.

Electric Field due to Infinite Wire

  1. Consider an infinitely long wire with a linear charge concentration. Due to the symmetry of the wire, we compute the electric field using a cylindrical Gaussian surface. 
  2. Since the field of electricity E is radial, flux via the end of the cylinder surface is zero, as the electrical field and the region vector are perpendicular. 
  3. The sole source of electric flux will be the curved Gaussian surface.

Electric Field due to Infinite Plate Sheet

  1. Gauss' law can be used to compute the electrical field of a continuous charge with an even linear charge density. 
  2. When viewing the Gaussian area in the shape of a cylindrical object with a radius of r, the field of electricity has an identical amplitude and radiates outward at all points of the cylinder.

Electric Field due to thin Spherical Shell

Take a thin round sphere with a radius of "R" and a surface charge density. The shell has spherical symmetry, as may be seen by looking at it. The electric field of a spherical shell can be calculated using two approaches-

  1. Electric Field Beyond the Spherical Shell.
  2. Electric Field within the Spherical Shell.

Read more about the Eddy Current.

How to Solve Problem applying Gauss's Law?

The following are some of the steps to follow while solving problems related to Gauss Law-

  1. Determine the pattern of the field lines using the charge distribution's symmetry.
  2. Selecting the Gaussian surface and the E, which should be either perpendicular to dS or should be parallel to dS
  3. If, in this case, E is perpendicular to dS, the magnitude of E must be uniform over this surface's portion. 
  4. After that, the integral is reduced to a sum of area elements.

Read More about- Limitations of Ohm's Law, Drift Velocity Formula and Electrical Insulator.

Points to Remember

  1. Gauss' law describes an electrical charge contained in the confined electrical charge that exists in the space inside the closed surface.
  2. The formula for the GAUSS LAW is: = Q/0. 
  3. where Q denotes the total charge on the given surface and 0 denotes the electric constant.
  4. According to Gauss's Law, the entire flux linked to a contained surface equals 1/0 times the charge enclosed by the enclosed surface.
  5. The electrical field flux from any given covered surface equates to the electrical charge contained by the surface, irrespective of how the charge is distributed, according to the formula.

Also read about- Law of Variable Proportion

Conclusion

Gauss' law depicts the connection between the magnetic field's charge distribution and the mobility of the electrolytic field in space. In accordance with Gaussian law, the extra charge would be fully on the surface of the conductor material, not within it. Keep in mind that this can only be true if solid conductors are electric and the ions plus valence electrons that make up the conductor don't move in a net electrical charge motion.

Suimilar read- Law of Variable Proportion

Frequently Asked Questions

What does Gauss Law state?

Gauss's law is a law in physics that relates the electric field to the electric charge. It states that the electric flux through a closed surface is proportional to the total electric charge enclosed by the surface.

Gauss law was discovered by whom?

Ans. Gauss law was first discovered in 1762 by Lagrange and by Gauss in 1813

What is Q in Gauss law?

Ans. Q or q is the charge enclosed in the volume.

Define Gaussian surface.

Ans. The Gaussian surface is an enclosed surface in space with three dimensions that can be used to compute the flux of a vector field.

What is Gauss law?

Ans. The flux of an electric field via any closed surface, commonly known as a Gaussian surface, is equivalent to the net charge encapsulated divided by free space permittivity.

What is the electric flux Class 12?

In physics, electric flux is the measure of the total electric field that passes through a surface. It is a vector quantity, and its direction is perpendicular to the surface. The SI unit of electric flux is the Weber (Wb).

What is application of gauss law?

Gauss's law is a powerful tool in electromagnetism that can be used to calculate the electric field due to a variety of charge distributions. Some of the applications of Gauss's law include: calculating the electric field due to a point charge, calculating the electric field due to a uniformly charged sphere, calculating the electric field due to a uniformly charged sheet, calculating the capacitance of a capacitor, calculating the electric field inside a conductor

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