Flux through hemisphere, frustum, and cone with uniform field

[stronghold.mr]

PREVIOUS POST ----https://www.physicsforums.com/showthread.php?t=165844
THIS POST HELP ME OUT TO SOME EXTENT BUT I AM STILL MESSED UP...

I am messed up with the concept of projection of area of different surfaces and flux through different surfaces...

Please someone explain it with some examples such as -

1. Hemisphere (I AM GETTING --- FLUX = E pi r^2 ) PLEASE CONFIRM
2. Frustum (not getting)
3. Cone (not getting)

we have to find flux through all these surfaces (The field E is uniform)

 

[momo1111]

sorry about my English ...
- What came in must come out ...
3.
this is your Diagram:
(N.B. the dots in the cone are just to give it shape)

E
-->.../.\
-->../...\
-->./...\ <---- cone
-->/____\___________ <- table

...
E
-->.../!
-->../.!
-->./..! <---- half cone
-->/__! ___________ <- table
you have a triangle so the flux is :(surface of triangle) * (E) = ...
you can work out the same with othe problems .

 

[stronghold.mr]

thanks for ur reply

but can u please explain it for frustum and hemisphere

not getting the answer in case of frustum

and please confirm hemisphere one

thanks

 

[momo1111]

What is the orientation of the hemisphere ?

case 1 :
flux = (surface of semi Circle )*E
or
case 2 :
flux = (surface of a Circle )*E