Why Gauss's law works when charge enclosed is not uniform?

[Jae]

This problem has charge that is not uniform in the inside, but it is still possible to find the electric field as a function of distance outside the slab using Gauss's law. How is this possible if the electric field is not uniform in the slab and plane? Wouldn't the electric field from the middle of the slab to the a x-distance d be different on both sides?

Once I did Gauss's law I got a correct solution of
(sigma + row_E) / 2(epsilon naught)

Thank you for answering this question.

Mentor's Note: Thread moved to Advanced Physics Homework from another forum, hence the lack of a template.

 

[BvU]

This problem has charge that is not uniform in the inside, but it is still possible to find the electric field as a function of distance outside the slab using Gauss's law. How is this possible if the electric field is not uniform in the slab and plane?

Gauss law has no restriction to uniform charge distributions. The electric field found doesn't have to be uniform either. Why do you think it would have to be ?

Wouldn't the electric field from the middle of the slab to the a x-distance d be different on both sides?

What do you mean with "the electric field from the middle of the slab to the a x-distance d" ?

 

[Jae]

Gauss law has no restriction to uniform charge distributions. The electric field found doesn't have to be uniform either. Why do you think it would have to be ?

What do you mean with "the electric field from the middle of the slab to the a x-distance d" ?

If Gauss's law calculates the net electric flux. I don't understand how it's possible that calculating the electric field if the surface does not have a uniform field.
I made a typo. I mean to say the x-direction from the middle of the slab. Sorry.

Thank you for helping.

 

[SammyS]

If Gauss's law calculates the net electric flux. I don't understand how it's possible that calculating the electric field if the surface does not have a uniform field.
I made a typo. I mean to say the x-direction from the middle of the slab. Sorry.

Thank you for helping.

Gauss's Law only finds the total flux through a closed surface.

If there is sufficient symmetry present, then it may be possible to determine the electric field on some portion of the surface.