Electric Field Flux Question

[member 757689]

Homework Statement

NA

Relevant Equations

NA

I'm not asking for a solution, but for one of my homework problems, it is asking about a circular surface and a positive charge to the right of the surface. I just wanted to check if the net electric flux through the loop would be zero, as the charge is not enclosed by the loop. Is there anything I'm missing here? Thank you for your help.

 

[DaveE]

You mean surface, not loop. right?
https://en.wikipedia.org/wiki/Gauss's_law

 

[haruspex]

it is asking about a circular surface

What is a circular surface? A sphere?

electric flux through the loop … the charge is not enclosed by the loop.

If it is a loop it cannot enclose anything. Only 2d manifolds (surfaces) can do that.

 

[member 757689]

If it is a loop it cannot enclose anything. Only 2d manifolds (surfaces) can do that.

Got it thank you, I meant like a disk but your second part helps.

 

[kuruman]

You can always calculate the flux through a circular disk of radius $r$ when charge $q$ on the axis of the disk at distance $z$. See diagram on the right. The disk (dotted line) can be considered to lie on the surface of a sphere of radius $R$ centered on charge $q$. You know that

• the electric field on the surface of the sphere is $E=\dfrac{q}{4\pi\epsilon_0R^2}.$
• all electric field lines that cross the surface of the disk must cross the surface of the spherical segment delimited by the dashed circle.
• $$\Phi_E=\int_S\mathbf E\cdot \mathbf{\hat n}~dA.$$

Can you do the last integral to find the flux?