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A cylindrical Gaussian surface is commonly used to calculate the electric charge of an infinitely long, straight, 'ideal' wire. A Gaussian surface is a closed surface in three-dimensional space through which the flux of a vector field is calculated; usually the gravitational field, electric field, or magnetic field. [1]
No charge is enclosed by the sphere. Electric flux through its surface is zero. Gauss's law may be expressed as: [6] = where Φ E is the electric flux through a closed surface S enclosing any volume V, Q is the total charge enclosed within V, and ε 0 is the electric constant.
The volume rate of flow of liquid through a source or sink (with the flow through a sink given a negative sign) is equal to the divergence of the velocity field at the pipe mouth, so adding up (integrating) the divergence of the liquid throughout the volume enclosed by S equals the volume rate of flux through S. This is the divergence theorem. [2]
For simplicity in calculations it is often convenient to consider a surface perpendicular to the flux lines. If the electric field is uniform, the electric flux passing through a surface of vector area A is = = , where E is the electric field (having the unit V/m), E is its magnitude, A is the area of the surface, and θ is the angle between ...
A perfect conductor has infinite conductivity, σ = ∞, while a perfect dielectric is a material that has no conductivity at all, σ = 0; this latter case, of real-valued permittivity (or complex-valued permittivity with zero imaginary component) is also associated with the name lossless media. [19]
In physics, Gauss's law for gravity, also known as Gauss's flux theorem for gravity, is a law of physics that is equivalent to Newton's law of universal gravitation. It is named after Carl Friedrich Gauss. It states that the flux (surface integral) of the gravitational field over any closed surface is proportional to the mass enclosed. Gauss's ...
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 ...
Outside of this wire the magnetic induction is zero, in contrast to the vector potential, which essentially depends on the magnetic flux through the cross-section of the wire and does not vanish outside. Since there is no electric field either, the Maxwell tensor F = 0 throughout the space-time region outside the tube, during the experiment ...