What is the concept of Gauss' physical law?

In summary: The curl (rotation) of the electric field around a loop is zero unless there is some magnetic flux through the loop. This is Faraday's law. You can also think of it this way: you don't have to use vectors to describe a static electric field. You can instead just consider the electrical potential at each point in space -- a scalar field. Any vector field that can be described this way must be curl-free via a simple theorem from vector calculus. The magnetic field, on the other hand, is never curl-free, and can never be described with "magnetic potentials."This is one of the core principles of electromagnetism. Essentially, it states that you can
  • #1
galipop
51
0
Can someone put into plain english the following points:

1. What is the concept of Gauss' physical law.

2. Why is the rotation of an electric field zero.

Cheers
 
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  • #2
1. Gauss' law simply says that the flux of the electric field through a surface is proportional to charge in the volume enclosed by that surface.

2. The curl (rotation) of the electric field around a loop is zero unless there is some magnetic flux through the loop. This is Faraday's law. You can also think of it this way: you don't have to use vectors to describe a static electric field. You can instead just consider the electrical potential at each point in space -- a scalar field. Any vector field that can be described this way must be curl-free via a simple theorem from vector calculus. The magnetic field, on the other hand, is never curl-free, and can never be described with "magnetic potentials."

- Warren
 
  • #3
1. What is the concept of Gauss' physical law.

Thinking about it in terms of the water faucet and sinks analogy has always helped me visualize what's happening. The electric field (the water) only flows out of faucets (concentrations of positive charge); while the water flows into sinks (concentrations of negative charge). The mathematical statement of Gauss's Law which Chroot detailed for you,

Gauss' law simply says that the flux of the electric field through a surface is proportional to charge in the volume enclosed by that surface.

is relating the sink or faucet, to what happens on a surface outside the sink or faucet. Let's make this abstract "surface" outside the sink or faucet a balloon with holes in it. Now stick a balloon with holes in it over a faucet that is turned on, and we all know what will happen. Water will "flux" (latin for flow) out of the balloon. Using some common sense, it should be obvious that you will be able to determine the rate water comes out of the tap from knowing the rate water comes out of the holes in the balloon. Remember from the analogy that the rate water comes out of the faucet is the representation of the amount of positive charge. The same thinking works for "sinks" as well (water flows through the balloon into the sink.) That is the relation between electric flux and charge (aka Gauss's Law.)
 

1. What is the concept of Gauss' physical law?

Gauss' physical law, also known as Gauss' law of electrostatics, is a fundamental law in electromagnetism that describes the relationship between electric charges and electric fields. It states that the electric flux through a closed surface is equal to the enclosed charge divided by the permittivity of free space.

2. What is the significance of Gauss' physical law?

Gauss' physical law is significant because it provides a quantitative description of the behavior of electric charges and electric fields. It is one of the four Maxwell's equations that form the foundation of classical electromagnetism and has numerous applications in engineering and physics.

3. How is Gauss' physical law derived?

Gauss' physical law is derived from Coulomb's law, which describes the force between two static charges. By applying the principles of vector calculus, such as divergence and the divergence theorem, Gauss' law can be mathematically derived from Coulomb's law.

4. What is the difference between Gauss' physical law and Gauss' law for magnetism?

Gauss' physical law describes the relationship between electric charges and electric fields, while Gauss' law for magnetism describes the relationship between magnetic fields and their sources. Unlike Gauss' physical law, Gauss' law for magnetism states that the magnetic flux through a closed surface is always zero, as there are no magnetic monopoles.

5. How is Gauss' physical law used in practical applications?

Gauss' physical law is used in a variety of practical applications, such as in electrical engineering for designing circuits, in the analysis of electromagnetic waves, and in the calculation of electric fields for charged particles. It is also used in the study of conductors and insulators, and in the design of electronic devices such as capacitors and antennas.

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