Electric Flux through an Infinite Plane

[julius71989]

Homework Statement

A point charge 60 microcoulomb is located in the origin. An infinite plane located at z=5. What is the electric flux in the plane due to the charge?

Q=60x10^-6 C at 0,0,0 (origin)
z=5 (plane)

Here, I consider the electric flux emanating from Q that passes through the z plane. Each radial electric field produced by the charge forms circle in the plane. I get the summation of each circle circumference's ratio with whole sphere to infinity.

But I got 1/(2xepsilon) times 60microcoulomb = 30/e(epsilon). I know I did not got the right answer cause the answer must be the half of the charge. Any Idea of solving the problem? help.

 

[Doc Al]

But I got 1/(2xepsilon) times 60microcoulomb = 30/e(epsilon). I know I did not got the right answer cause the answer must be the half of the charge.

What do you mean that the answer must be half the charge? Gauss's law tells us that the total flux from the charge is $$Q/\epsilon_0$$; what's half of that? (You've got it right.)

 

[Defennder]

How do we use Gauss law here? It isn't an enclosed surface. I integrated it directly to get $$\frac{q}{2\varepsilon_0}$$.

 

[Doc Al]

How do we use Gauss law here? It isn't an enclosed surface.

Just imagine one: A spherical surface surrounding the point charge. Clearly all "field lines" from one half of the sphere will pass through that plane.

I integrated it directly to get $$\frac{q}{2\varepsilon_0}$$.

Nothing wrong with doing it the hard way.

 

[Defennder]

Oh I see. Thanks.