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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.
Electric field from positive to negative charges. Gauss's law describes the relationship between an electric field and electric charges: an electric field points away from positive charges and towards negative charges, and the net outflow of the electric field through a closed surface is proportional to the enclosed charge, including bound charge due to polarization of material.
The source free equations can be written by the action of the exterior derivative on this 2-form. But for the equations with source terms (Gauss's law and the Ampère-Maxwell equation), the Hodge dual of this 2-form is needed. The Hodge star operator takes a p-form to a (n − p)-form, where n is the number of dimensions.
The resulting two equations (Gauss's law = and Faraday's law with no induction term =), taken together, are equivalent to Coulomb's law, which states that a particle with electric charge at position exerts a force on a particle with charge at position of: [13] = ^ | | = | | where
That equation is another way of writing the two inhomogeneous Maxwell's equations (namely, Gauss's law and Ampère's circuital law) using the substitutions: = = where i, j, k take the values 1, 2, and 3.
In electromagnetism, electric flux is the total electric field that crosses a given surface. [1] The electric flux through a closed surface is equal to the total charge contained within that surface. The electric field E can exert a force on an electric charge at any point in space. The electric field is the gradient of the electric potential.
Position vector r is a point to calculate the electric field; r′ is a point in the charged object. Contrary to the strong analogy between (classical) gravitation and electrostatics, there are no "centre of charge" or "centre of electrostatic attraction" analogues. [citation needed] Electric transport
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 ...