## Quick Reference

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 **& #x222B;s**

*V*⋅

*n*∧d

*S*=&

*#*

*x*222

*B*;

*V*⋅d

*S*. 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

*∫*

_{S}*V*× d

*S*and for the scalar function ɸ(

*x*,

*y*,

*z*) the surface integral

*∫*

*ɸd*

_{S}*S*.

*Subjects:*
Physics.

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