Maxwell's, integrals, current, elements, delta phi and confusion

[OJFord]

I'm working on an online EECS course, and to be frank some of it is going straight over my head - but at the same time parts of it are far below my current knowledge, so I want to work and stick with it.


The speaker is working through proving current and voltage - to arrive at Kirchoff's laws as far as I can tell (though I haven't got that far).


The first thing that threw me was this talk of 'elements' - does he mean elements as in periodic? Or as in a sub-class of something, a circuit, anything?

He says that a basic rule is defined such that all elements must obey:

$\frac{\delta\phi B}{\delta t} = 0$

Otherwise they are not allowed, and by doing this it means that the mathematics works out okay, and we can calculate properties easily.

But what does it mean for del phi B by del t to equal 0? What are B and t?


Are they properties of materials that make - say, silicon - suitable for use in electronic circuits?



My second question regards integrating notation. I haven't come across integrals with the following notation yet, and I hope someone can explain:

1) $\oint$

(ie, what's the difference with the addition of the circle/loop in the center?)

2) $\int_{ab}$ or $\int_{\delta c}$

(ie, what does it mean to only have a lower limit? Or is the first the lower and second the upper, and in the case of delta c, the limits are the difference represented by the delta - ie if it were say dl, showing extension, the lower limit would be original and the upper the extended length?)

3) $\int\int$ or $\oint\oint$

(I assume these are for 'second integrals', much like d^2y/dx^2?)



Thanks in advance for any help on either question.

 

[leright]

I'm working on an online EECS course, and to be frank some of it is going straight over my head - but at the same time parts of it are far below my current knowledge, so I want to work and stick with it.The speaker is working through proving current and voltage - to arrive at Kirchoff's laws as far as I can tell (though I haven't got that far).The first thing that threw me was this talk of 'elements' - does he mean elements as in periodic? Or as in a sub-class of something, a circuit, anything?

He says that a basic rule is defined such that all elements must obey:

$\frac{\delta\phi B}{\delta t} = 0$

Otherwise they are not allowed, and by doing this it means that the mathematics works out okay, and we can calculate properties easily.

But what does it mean for del phi B by del t to equal 0? What are B and t?Are they properties of materials that make - say, silicon - suitable for use in electronic circuits?
My second question regards integrating notation. I haven't come across integrals with the following notation yet, and I hope someone can explain:

1) $\oint$

(ie, what's the difference with the addition of the circle/loop in the center?)

2) $\int_{ab}$ or $\int_{\delta c}$

(ie, what does it mean to only have a lower limit? Or is the first the lower and second the upper, and in the case of delta c, the limits are the difference represented by the delta - ie if it were say dl, showing extension, the lower limit would be original and the upper the extended length?)

3) $\int\int$ or $\oint\oint$

(I assume these are for 'second integrals', much like d^2y/dx^2?)
Thanks in advance for any help on either question.

1.) He probably means circuit elements when he says 'elements'...like resistors, inductors, and capacitors.

2.) In dB/dt = 0, B is the magnetic flux density and t is time. This means that the magnetic flux density is constant wrt time. This is needs to be true for kirchhoffs voltage law to be true, otherwise you get non conservative electric fields invalidating KVL.

3.) The integral symbol with the circle denotes a path integral around a closed loop.

4.) The integral symbol with ab at the bottom denotes a path integral from points a to b.

5.) the double integrall symbols are for when integrating a surface and the triple integrals are for wen integrating a volume.

-Matt Leright

 

[OJFord]

Thanks for your response.

2) So is that a material or component property? ie. by material I mean is that why silicon is used, or by component I mean would it be a consideration if I were a company manufacturing resistors?

3) Is a path integral the same as a line integral? And what's the difference between this and a 'standard' integral that I'm used to seeing?

4) Even without the loop in the middle? I would ask more about this but I feel the answer is probably obvious to me when I understand the answer to my question 3).
Thanks again.

 

[yungman]

Thanks for your response.

2) So is that a material or component property? ie. by material I mean is that why silicon is used, or by component I mean would it be a consideration if I were a company manufacturing resistors?
No, it is just stating that there is no varying magnetic field.
3) Is a path integral the same as a line integral? And what's the difference between this and a 'standard' integral that I'm used to seeing?
Yes, but the integral sign with a circle means that the path is a closed path...like a circle where the end of the path is the beginning of the path.
4) Even without the loop in the middle? I would ask more about this but I feel the answer is probably obvious to me when I understand the answer to my question 3).



Thanks again.

Say if you have a line integral: $\int_{ab}$ implies you integrate from point a to point b. But if point b is equal to point a, then you have a closed path. Then instead, you put a circle on the integral.

 

[leright]

the circle can also indicate an integral on a closed surface...like a sphere,

 

[yungman]

You are right,

Usually books use $\oint_c \;$ for line integral for closed path. $\oint_s \;$ is for closed surface.