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David W. Sutherland _________________________________________________________ dws3963

Week 12____________________________________________________________________7.5.7

http://hotard108.tripod.com/311hwk12b.html

Let B = delta X A be a magnetic field, and S a surface. Consider the flux of B through the surface.

a) Describe a scenario in which Guass's theorem would enable you to evaluate the flux integral.

Gauss's theorem would enable you to evaluate the flux integral only if the surface is closed. So, this would apply if the surface was a sphere, or a cube, or a parallelipiped. A physical example would be calculating the flux through a balloon adjacent to a power line.

b) Describe a scenario in which Stokes' theorem would enable you to evaluate the flux integral.

Stokes' theorem relates a surface integral over a surface S to a line integral around the boundary curve of S. So, for it to be used, S must be a smooth surface bounded by a closed boundary curve. One example of a applicable surface would be an open hemisphere.