Difference Between Gauss's Law and Electric Flux

 Gauss's Law

A fundamental idea in electromagnetism known as Gauss' law connects the charge contained within a closed surface to the electric flux passing through the surface. The rule bears Carl Friedrich Gauss' name, a German scientist and mathematician.

Gauss's law states that

The electric flux through any closed surface is proportional to the total charge enclosed within the surface. The electric flux is the flow of electric field through a surface, and it is calculated by taking the dot product of the electric field and the surface area element.

 The law can be mathematically expressed as:

 

Φ = ∫ E · dA = Q/ε₀

 

Where

• Φ = electric flux
• E = electric field
• dA = surface area element
• Q = charge enclosed within the surface
• ε₀ = electric constant

The electric field may be calculated using Gauss's formula for a variety of issues, such as determining the field of a charged sphere, cylinder, or plane. The law is very helpful in high symmetry issues since it makes it simpler to compute the flux because the electric field has a uniform direction throughout the surface.

 

The electric field may be calculated using Gauss's formula in a number of settings, and it is crucial to comprehending many electromagnetic topics, including electrostatics, electric potential, and electric currents.

Electric Flux

It states that

Electric flux is a measure of the flow of electric field through a surface. The dot product of the electric field and the surface area element is used to compute it as a scalar quantity.

Mathematically, the electric flux Φ through a surface S is given by the equation:

 

Φ = ∫∫S E · dA

 

Here,

•  E = electric field,
• dA = surface area element, and the integral is taken over the entire surface S.

The dot product E · dA represents the component of the electric field that is perpendicular to the surface, multiplied by the area of the surface.

Therefore, the electric flux is a measure of the number of electric field lines passing through the surface.

The entire quantity of charge contained inside the surface affects the electric flux in a direct proportion. The electric flux across a closed surface is equal to the total charge contained inside the surface, divided by the electric constant 0. This is known as Gauss's law. This may be written mathematically as:

Φ = Q/ε0

 

Where

•  Q = total charge enclosed within the closed surface

 

Calculating the electric field caused by charged objects with great symmetry, such as spheres, cylinders, and planes, requires understanding the idea of electric flux, which is crucial to understanding electromagnetism. It may be used to calculate the charge distribution on a conductor and is also used to comprehend how electric fields behave in conductors and insulators. In general, electric flux is a fundamental idea in electromagnetism that is crucial for comprehending a variety of physics processes.