Understanding Gauss' Law for Electric Fields

[sponsoredwalk]

Hi I'm just making sure I'm understanding the information I'm getting from
"A Student's Guide to Maxwell's Equations"
The book is talking about Gauss' Law for Electric Fields

$$\bold{E\cdot n}\;\; = E cos (90) = 0$$

Does this mean that the full electric field is going through the surface?

Could you mention maybe one or two examples of when this happens?

What does it mean to say it's at a 30 degree angle,
is some of the electric field coming out?

Could you also mention maybe one or two examples of when this happens?

How can that be when Gauss' Law for Electric Fields
concerns a closed surface?

I'm really only beginning this Maxwell's equations properly and am unsure of what some of it means.

(: Please Let Me Know, Gratias Vobis Ago :)

 

[berkeman]

Hi I'm just making sure I'm understanding the information I'm getting from
"A Student's Guide to Maxwell's Equations"
The book is talking about Gauss' Law for Electric Fields

$$\bold{E\cdot n}\;\; = E cos (90) = 0$$

Does this mean that the full electric field is going through the surface?

Could you mention maybe one or two examples of when this happens?

What does it mean to say it's at a 30 degree angle,
is some of the electric field coming out?

Could you also mention maybe one or two examples of when this happens?

How can that be when Gauss' Law for Electric Fields
concerns a closed surface?

I'm really only beginning this Maxwell's equations properly and am unsure of what some of it means.

(: Please Let Me Know, Gratias Vobis Ago :)

The wikipedia page on Gauss' Law is a pretty good intro, with some good links to other sources (including the MIT video lecture series). Be sure to click on the Gaussian Surface link near the bottom -- it has some examples that should help you.

One of the examples is the Gaussian Pillbox -- that can be configured to give you surfaces where the E field is perpendicular to some of the surfaces, but parallel to others, which seems to be part of what you are asking about.

 

[Redbelly98]

Hi I'm just making sure I'm understanding the information I'm getting from
"A Student's Guide to Maxwell's Equations"
The book is talking about Gauss' Law for Electric Fields

$$\bold{E\cdot n}\;\; = E cos (90) = 0$$

Does this mean that the full electric field is going through the surface?

Actually, it means E is parallel to the surface.

n is the unit vector perpendicular to the surface, so if E is at 90° to n then it is parallel to the surface.

0° would mean E is perpendicular to the surface.

 

[sponsoredwalk]

Thanks Berkeman but I'm hardly asking a homework question or trying to cheat, I'm quoting an example from the book I mentioned and since I have no teacher nor physics friend to clarify a quick question I'd rather ask for help than learn something incorrectly. I have a book and the wikipedia article is too advanced. As regards the Gaussian Pillbox I have no idea what that means and my book has no mention of it.

I'd just like to know if I'm picturing what my book is describing correctly...

 

[sponsoredwalk]

So E = cos(90) mean that the electric field is going through the surface.
So then the surface is electrified.

Is this how the tiny copper wires inside of telephone cables and plug sockets work?
(My book hasn't mentioned plug sockets or any example so I'm going off logic)

What does it mean to say it's at a 30' Angle, does this mean the field is going from the top of the sphere to the bottom, like in those pictures of the magnetic poles of the Earth with the lines of force exuding from the top of the globe to the bottom

Again I apologise for asking but If I don't I'll end up learning this stuff wrong

 

[berkeman]

So E = cos(90) mean that the electric field is going through the surface.
So then the surface is electrified.

Is this how the tiny copper wires inside of telephone cables and plug sockets work?
(My book hasn't mentioned plug sockets or any example so I'm going off logic)

What does it mean to say it's at a 30' Angle, does this mean the field is going from the top of the sphere to the bottom, like in those pictures of the magnetic poles of the Earth with the lines of force exuding from the top of the globe to the bottom

Again I apologise for asking but If I don't I'll end up learning this stuff wrong

Ah, I understand better now. It may be that you are trying to self-study from a book without having self-studied the "prerequisites" first. Gauss' Law deals with a vector equation and integration, which would have prerequisites of some trig, vectors, and calculus. I'm not sure it's productive to be trying to self-study Gauss' Law, without having studied and understood some from those three subjects at least.

And it might be good to step back and study some basic electronics stuff first, like resistors, capacitors, inductors, circuits, etc. It will make learning E&M much more real, if you have a basic understanding of circuits first. Then you would not have to be struggling with things like your questions:

So E = cos(90) mean that the electric field is going through the surface.
So then the surface is electrified.

Is this how the tiny copper wires inside of telephone cables and plug sockets work?

What is your overall goal in your studies? What-all have you studied so far, and what do you want to study next? Perhaps we can help guide you some in this.

 

[sponsoredwalk]

I' doing fine teaching myself Classical Mechanics, Linear Algebra, Calculus I & II (still not good enough at some integration aspects unfortunately lol), I get pretty far when I attempt stuff out of my league, I got pretty far into calculus without knowing what arctan meant but I've gone back and I'm just cleaning up the last of my previously shady masic math skills...

I'm doing fine but as you clearly see I'm still not confident enough not to second guess some basic things.

I am doing fine learning from the book I mentioned up top so far so I'll continue going, really I just wanted to get an answer to my question so I could be confident that I'm not learning this incorrectly.

So E = cos(90) mean that the electric field is going through the surface.
So then the surface is electrified.

Is this how the tiny copper wires inside of telephone cables and plug sockets work?
(My book hasn't mentioned plug sockets or any example so I'm going off logic)

What does it mean to say it's at a 30' Angle, does this mean the field is going from the top of the sphere to the bottom, like in those pictures of the magnetic poles of the Earth with the lines of force exuding from the top of the globe to the bottom


(:Again Thanks for any help :)

 

[berkeman]

So E = cos(90) mean that the electric field is going through the surface.
So then the surface is electrified.

No. "Electrofied" is an imprecise term. At best, it means that a conducting surface has an electric potential (a voltage) with respect to another conducting surface. Gauss' Law is not constrained to multiple conducting surfaces. It deals at a fundamental level with how charged particles generate E-fields in 3-dimensions. If you have a Gaussian Pillbox sitting on a table (all non-conducting), and you have a vertical E-field, then that E-field pierces the top and bottom of the box with a 90 degree angle (parallel or anti-parallel to the normal unit vector for each surface), and flows by the other 4 sides parallel (0 degree angle).

Is this how the tiny copper wires inside of telephone cables and plug sockets work?

Not for the most part. Gauss' Law has its uses, but not primarily in simple RLC circuits.