To find the flow of the field
across the surface of the cone with 0 < z < H
a) Directly
b) Applying Gauss's theorem
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"?