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Gauss's law in its integral form is particularly useful when, by symmetry reasons, a closed surface (GS) can be found along which the electric field is uniform. The electric flux is then a simple product of the surface area and the strength of the electric field, and is proportional to the total charge enclosed by the surface.
If magnetic monopoles were to be discovered, then Gauss's law for magnetism would state the divergence of B would be proportional to the magnetic charge density ρ m, analogous to Gauss's law for electric field. For zero net magnetic charge density (ρ m = 0), the original form of Gauss's magnetism law is the result.
While Gauss's law holds for all situations, it is most useful for "by hand" calculations when high degrees of symmetry exist in the electric field. Examples include spherical and cylindrical symmetry. The SI unit of electric flux is the volt-meter (V·m), or, equivalently, newton-meter squared per coulomb (N·m 2 ·C −1).
A parallel plate capacitor. Using an imaginary box, it is possible to use Gauss's law to explain the relationship between electric displacement and free charge. Consider an infinite parallel plate capacitor where the space between the plates is empty or contains a neutral, insulating medium. In both cases, the free charges are only on the metal ...
It is an arbitrary closed surface S = ∂V (the boundary of a 3-dimensional region V) used in conjunction with Gauss's law for the corresponding field (Gauss's law, Gauss's law for magnetism, or Gauss's law for gravity) by performing a surface integral, in order to calculate the total amount of the source quantity enclosed; e.g., amount of ...
The difference in the oscillations when the bar was magnetised and when it was demagnetised allowed Gauss to calculate an absolute value for the strength of the Earth's magnetic field. [9] The gauss, the CGS unit of magnetic flux density was named in his honour, defined as one maxwell per square centimeter; it equals 1×10 −4 tesla (the SI ...
Gauss's law for magnetism, one of Maxwell's equations, is the mathematical statement that magnetic monopoles do not exist. Nevertheless, Pierre Curie pointed out in 1894 [ 9 ] that magnetic monopoles could conceivably exist, despite not having been seen so far.
Using the right hand rule to find the direction of the magnetic field. The direction of the magnetic field at a point, the direction of the arrowheads on the magnetic field lines, which is the direction that the "north pole" of the compass needle points, can be found from the current by the right-hand rule.