Can Gauss' Law Be Applied Here?

[Taulant Sholla]

Homework Statement

Homework Equations

Gauss' Law: ∫E⋅da = q_enc/ε₀
E-field: E = kq/r²

The Attempt at a Solution

I solved this using electric field equation, differential elements, and integration. The correct answer is, I think, E=-q/(8πε₀R²)

QUESTION: Can this be done via Gauss' Law? The source charge itself is a "cup surface." Here's my attempt...

 

[BvU]

I solved this using electric field equation, differential elements, and integration

And which way is that $\vec E$ pointing ? What is the $R$ there ?

The E you calculate using Gauss law, is it the same everywhere ? Pointing which way ?

 

[SammyS]

Homework Statement

View attachment 95494

Homework Equations

Gauss' Law: ∫E⋅da = q_enc/ε₀
E-field: E = kq/r²

The Attempt at a Solution

I solved this using electric field equation, differential elements, and integration. The correct answer is, I think, E=-q/(8πε₀R²)

QUESTION: Can this be done via Gauss' Law? The source charge itself is a "cup surface." Here's my attempt...
View attachment 95495

I know of no way to use Gauss's Law to solve for E at the center. There's not the required symmetry.

What are the requirements for using Gauss's Law for such a purpose?

 

[Taulant Sholla]

There are no requirements to use Gauss' Law. I was wondering if it is possible. I assume since the source charge is asymmetrical, Gauss' Law can't be applied?

 

[SammyS]

There are no requirements to use Gauss' Law. I was wondering if it is possible. I assume since the source charge is asymmetrical, Gauss' Law can't be applied?

If you're calculating flux from knowledge of the charge distribution, or vice versa, then you're correct.

However, if you use it to get the field from the charge distribution, there are requirements, involving symmetry, as well as the Gaussian surface which takes advantage of that symmetry.

 

[Taulant Sholla]

okay, thank you very much!