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surface integral


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An integral taken over a surface that can involve vectors or scalars. If V(x,y,z) is a vector function defined in a region that contains the surface S and the unit vector n∧ is defined as the (outward) normal to that surface, the surface integral is defined by ∫sVn∧dS=∫V⋅dS. This integral is the (outward) flux of V through S. Surface integrals for flux occur in electricity and magnetism, an example being Gauss' law. It is also possible to define the surface integral SV × dS and for the scalar function ɸ(x,y,z) the surface integral SɸdS.

Subjects: Physics.


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