To find the flow of the field

across the surface of the cone with 0 < z < H

a) Directly

b) Applying Gauss's theorem

(Talking)

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- Jul 18th 2010, 03:16 PMrikelme23Surface integral solved directly and using Gauss' Theorem.
To find the flow of the field

across the surface of the cone with 0 < z < H

a) Directly

b) Applying Gauss's theorem

(Talking) - Jul 19th 2010, 05:10 AMHallsofIvy
What have

**you**tried?

I will give you this much: we can write the cone in parametric coordinates using polar coordinates: , , with from 0 to H and [/tex]\theta[/tex] from 0 to .

With that you can write the "position vector" of a point on the surface of the cone as .

The deriviatives of that with respect to r and :

and

are in the tangent plane to the cone and their cross product is

.

The (upward oriented) "vector differential of area" is

Take the dot product of your field with that and integrate.

And what**is**"Gauss's theorem"?