Question

Hi
A question?

Answer 1

can explain how this two sides are equal?\[\cos \theta da=r^2d \Omega\]

Answer 2

where da is surface element in spherical coordinate & omeg is solid angle

Answer 3

It looks wrong. If you integrate over the entire sphere, the right hand side is
\[ 4 \pi r^2 \]
but the left hand side is
\[ 8 \pi r^2 \]

Answer 4

it's in classical electrodynamics (by Jackson)page28

Answer 5

I think this is the same formula we are finding in figure 4.2.4 on this page
http://ocw.mit.edu/courses/physics/8-02sc-physics-ii-electricity-and-magnetism-fall-2010/conductors-and-insulators-conductors-as-shields/MIT8_02SC_notes9.pdf
though the area is not represented as a differential here. I trust that James' math is right though, so that must have some change in the problem.

Answer 6

r square* d(sigma) = r*d(theta) *r*d(phi) =projection of area element=dA cos(theta) ....in azimuthal coordinates..