How Do You Calculate Electric Flux Through a Paraboloidal Surface?

[TheChicken]

Homework Statement

http://img362.imageshack.us/img362/8044/p2413zn4.gif

Calculate the total electric flux through the paraboloidal surface due to a constant electric field of magnitude E0 in the direction shown in Figure P24.13. (Use E_0 for E0, and r and d as necessary.)

Homework Equations

E = (ke +q-q)/r²
flux = EA cos theta
flux = Q/ e_0

The Attempt at a Solution

I have no idea how to solve this problem, or any other problems on this assignment for that matter. This seems to be beyond what the book actually covers, and I have no idea what to do. Any help is greatly appreciated.

 

[dynamicsolo]

Ah, you have had Gauss' Law: that's the third equation you wrote (flux = Q/ e_0).

What does Q represent in that equation? What is the value of "Q" for the volume inside the paraboloid surface?

 

[cepheid]

Yeah, this vector field has no divergence due to a lack of sources or sinks. If you don't know what I'm talking about, nevermind, and just listen to dynamicsolo. But if you've seen Gauss' Law in differential form, then you'll see what I mean.

 

[TheChicken]

But it's like... it's such a bizarre shape. I tried entering in "E_0((4/3)r^2d)" and that didn't get me anywhere. And even then, when you have the volume, if the electric field is E_0, does that mean it's E_0 per meter cubed?

I know that flux is EA cos theta, but you have to do some ridiculous integrating or something to solve for a 'paraboloid' using that formula.

 

[Defennder]

You don't have to do any calculation at all if you employ Gauss law wisely. Read through dynamicsolo's post for hints on how to do so.

 

[dynamicsolo]

Well, you have to do a little calculation, but no integrating at all. Ask yourself this: what is the total electric flux through the entire body of this bullet-shaped surface? Then, what is the electric flux through the circular face at one end of the surface? What then must be the flux through the paraboloidal end?

And, yes, it is a bizarre shape -- that's deliberate. In an introductory physics course, that's often a sign in a problem that you're supposed to use a concept, rather than a difficult computation...