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The magnetic flux density (magnetic field) having the unit Wb/m 2 is denoted by B, and magnetic flux is defined analogously: [13] [14] = with the same notation above. The quantity arises in Faraday's law of induction , where the magnetic flux is time-dependent either because the boundary is time-dependent or magnetic field is time-dependent.
In mathematical terms, Alfvén's theorem states that, in an electrically conducting fluid in the limit of a large magnetic Reynolds number, the magnetic flux Φ B through an orientable, open material surface advected by a macroscopic, space- and time-dependent velocity field [note 1] v is constant, or
In physics (specifically electromagnetism), Gauss's law, also known as Gauss's flux theorem (or sometimes Gauss's theorem), is one of Maxwell's equations. It is an application of the divergence theorem , and it relates the distribution of electric charge to the resulting electric field .
At right the two subvolumes are separated to show the flux out of the different surfaces. See the diagram. A closed, bounded volume V is divided into two volumes V 1 and V 2 by a surface S 3 (green). The flux Φ(V i) out of each component region V i is equal to the sum of the flux through its two faces, so the sum of the flux out of the two ...
All of the conservation laws listed above are local conservation laws. A local conservation law is expressed mathematically by a continuity equation, which states that the change in the quantity in a volume is equal to the total net "flux" of the quantity through the surface of the volume. The following sections discuss continuity equations in ...
This has to hold simultaneously for every possible volume V; the only way this can happen is if the integrands are equal. Hence we arrive at ∇ ⋅ g = − 4 π G ρ , {\displaystyle \nabla \cdot \mathbf {g} =-4\pi G\rho ,} which is the differential form of Gauss's law for gravity.
With no obvious options, China appears to be keeping its distance as Russia and North Korea move closer to each other with a new defense pact that could tilt the balance of power among the three ...
The Reynolds number can be defined for several different situations where a fluid is in relative motion to a surface. [n 1] These definitions generally include the fluid properties of density and viscosity, plus a velocity and a characteristic length or characteristic dimension (L in the above equation). This dimension is a matter of convention ...