Gauss' Law for Non-Uniform electric fields

[Dev]

Homework Statement

Please see image.

Relevant Equations

Nil.

The answer key shows option D is correct. But I think option C is also correct. Which option is correct here?

 

[Orodruin]

Only c is correct.

What makes d incorrect is the statement that the field is uniform on the surface.

 

[Dev]

Only c is correct.

What makes d incorrect is the statement that the field is uniform on the surface.

So, the field is not necessarily uniform on the Gaussian surface?

 

[Orodruin]

Definitely not.

 

[Orodruin]

… and let me add that you should probably find better sources to learn from given these basic errors you are encountering.

 

[Dev]

Can I trust this site blindly?

 

[Orodruin]

Can I trust this site blindly?

Blindly? No. You should never trust anything blindly.

PF is a site of volunteers. People make mistakes and some people answer questions they do not have the background to answer correctly.

Overall though, PF has many active and retired physicist, engineers, and scientists from other fields. Most of the time, errors will be corrected.

If in doubt, ask for clarification.

 

[Orodruin]

Also, PF, while great for getting questions answered, is not source material. It cannot fill the function of a textbook.

 

[Dev]

Also, PF, while great for getting questions answered, is not source material. It cannot fill the function of a textbook.

Can I trust you blindly, sir?

 

[Orodruin]

No. As I said, you cannot trust anything blindly.

I am human. I make mistakes. (Chatbots also make mistakes, usually loads of them)
I authored an 800 page textbook on mathematical methods in physics. Obviously it is going to have typos in it. What makes it a better or worse source is the quality of the text, but also the severity and frequency of the typos and other errors.

The sources you are quoting are making serious and seemingly frequent errors. This makes them bad sources.

You need to develop and apply critical thinking and ask for clarification and reasoning if there is something you don’t understand.

 

[PeroK]

Can I trust this site blindly?

You shouldn't trust anything blindly, but you should be able to decide to what extent a source is reliable. PF has the advantage that if someone makes a mistake, someone else will probably notice.

 

[kuruman]

Only c is correct.

Why is (a) incorrect?
You can have a surface element $dA$ (nobody said anything about integrating over a closed surface) with charges at some distance from the surface, one inside and the other outside, such that $(\mathbf E_1+\mathbf E_2)\cdot \mathbf{\hat n}~dA \neq 0.$ Both charges contribute to the electric flux through $dA.$

 

[PeroK]

a) and b) have to be read as "total" electric flux through the surface to be false!

 

[kuruman]

a) and b) have to be read as "total" electric flex through the surface to be false!

You mean misread total electric "flex" as total electric "flux".

 

[PeroK]

You mean misread total electric "flex" as total electric "flux".

Perhaps a flex is a flux line?

 

[kuruman]

Perhaps a flex is a flux line?

Sounds about right for a flux line associated with the divergence. A line associated with the curl would be a circumflex.

I stop here lest the mentors lock this thread for silliness.

 

[WWGD]

Can I trust you blindly, sir?

Yes. Deposit all your money on my account ABC001954 in Banesco, Brickell Avenue 33091 .

 

[Orodruin]

Why is (a) incorrect?
You can have a surface element $dA$ (nobody said anything about integrating over a closed surface) with charges at some distance from the surface, one inside and the other outside, such that $(\mathbf E_1+\mathbf E_2)\cdot \mathbf{\hat n}~dA \neq 0.$ Both charges contribute to the electric flux through $dA.$

The question pertains to Gauss’ law. The surface is closed and Gauss’ law relates to the total flux through a closed surface.