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Larmor formula; Lenz law; ... No charge is enclosed by the sphere. Electric flux through its surface is zero. ... and ρ free is the free electric charge density.
In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in coulombs per cubic meter (C⋅m −3), at any point in a volume.
According to Gauss’s law, a conductor at equilibrium carrying an applied current has no charge on its interior.Instead, the entirety of the charge of the conductor resides on the surface, and can be expressed by the equation: = where E is the electric field caused by the charge on the conductor and is the permittivity of the free space.
an infinite plane of uniform charge; an infinitely long cylinder of uniform charge; As example "field near infinite line charge" is given below; Consider a point P at a distance r from an infinite line charge having charge density (charge per unit length) λ. Imagine a closed surface in the form of cylinder whose axis of rotation is the line ...
The potential inside the sphere is thus given by the above expression for the potential of the two charges. This potential will not be valid outside the sphere, since the image charge does not actually exist, but is rather "standing in" for the surface charge densities induced on the sphere by the inner charge at . The potential outside the ...
Since the integral equals the complex conjugate of the interior multipole moments of the second (peripheral) charge distribution, the energy formula reduces to the simple form = = = For example, this formula may be used to determine the electrostatic interaction energies of the atomic nucleus with its surrounding electronic orbitals.
The Poisson–Boltzmann equation can also be used to calculate the electrostatic free energy for hypothetically charging a sphere using the following charging integral: = (′) ′ where is the final charge on the sphere The electrostatic free energy can also be expressed by taking the process of the charging system.
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 capacitor plates.