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In physical terms, the divergence of a vector field is the extent to which the vector field flux behaves like a source or a sink at a given point. It is a local measure of its "outgoingness" – the extent to which there are more of the field vectors exiting from an infinitesimal region of space than entering it.
The divergence at a point represents the degree to which a small volume around the point is a source or a sink for the vector flow, a result which is made precise by the divergence theorem. The divergence can also be defined on a Riemannian manifold, that is, a manifold with a Riemannian metric that measures the length of vectors.
A branch of physics that studies atoms as isolated systems of electrons and an atomic nucleus. Compare nuclear physics. atomic structure atomic weight (A) The sum total of protons (or electrons) and neutrons within an atom. audio frequency A periodic vibration whose frequency is in the band audible to the average human, the human hearing range.
The divergence theorem is an important result for the mathematics of physics and engineering, particularly in electrostatics and fluid dynamics. In these fields, it is usually applied in three dimensions. However, it generalizes to any number of dimensions. In one dimension, it is equivalent to the fundamental theorem of calculus.
D: divergence, C: curl, G: gradient, L: Laplacian, CC: curl of curl. Each arrow is labeled with the result of an identity, specifically, the result of applying the operator at the arrow's tail to the operator at its head. The blue circle in the middle means curl of curl exists, whereas the other two red circles (dashed) mean that DD and GG do ...
This means that the force field lines around the particle's equilibrium position should all point inward, toward that position. If all of the surrounding field lines point toward the equilibrium point, then the divergence of the field at that point must be negative (i.e. that point acts as a sink). However, Gauss's law says that the divergence ...
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.
[citation needed] This is why the magnetic field, characterized by zero divergence, can be expressed as the curl of a magnetic vector potential. If W is a vector field with curl( W ) = V , then adding any gradient vector field grad( f ) to W will result in another vector field W + grad( f ) such that curl( W + grad( f )) = V as well.