There's a singularity in ##\vec{E}## at r=0 you need to account for.nenyan said:Homework Statement
Gauss Divergence Law:
Gauss' law
Can we obtain the Gauss' Law from Gauss Divergence Law?
Homework Equations
In Spherical coordinates,
electric field strength
(Q/4[itex]\pi[/itex]εr^2,0,0)
Then ∇[itex]\cdot[/itex]E=0+0+0=0
The Attempt at a Solution
We can not obtain the Gauss' Law from the general mathematical law?
Gauss' law is a fundamental law in electromagnetism that relates the electric flux through a closed surface to the charge enclosed within the surface. Gauss Divergence Law, also known as the Divergence Theorem, is a mathematical theorem that relates the flux of a vector field through a closed surface to the divergence of the field within the surface.
Deducing Gauss' law from Gauss Divergence Law allows us to understand the fundamental relationship between the electric field and charge distribution in a given system. It also provides a powerful tool for solving complex electromagnetism problems.
The steps to deduce Gauss' law from Gauss Divergence Law are as follows: 1. Choose a Gaussian surface that encloses the charge distribution.2. Apply Gauss Divergence Law to the electric field and simplify using the properties of the divergence operator.3. Use the symmetry of the charge distribution to simplify the integral.4. Solve for the electric flux through the Gaussian surface.5. Equate the electric flux to the charge enclosed within the surface to obtain Gauss' law.
Yes, Gauss' law can be used to calculate the electric field for any charge distribution as long as the charge distribution has sufficient symmetry to simplify the integral.
Gauss' law and Gauss Divergence Law have various practical applications in the fields of electromagnetism, fluid mechanics, and heat transfer. They are used to calculate electric fields, magnetic fields, fluid flow, and heat transfer in various systems. They are also used in the design and analysis of electronic devices, such as capacitors and antennas.