# Search results

1. ### Prove Vector Quadruple Product with Levi-Civita/Index Notation

The given equation is correct: ##\qquad\qquad(\vec A \times \vec B)\times(\vec C \times \vec D) = [ \vec A \cdot (\vec B \times \vec D) ] \vec C - [ \vec A \cdot (\vec B \times \vec C) ] \vec D## The result I got was ##\qquad\qquad(\vec A \times \vec B)\times(\vec C \times \vec D) = [ \vec A...
2. ### Prove Vector Quadruple Product with Levi-Civita/Index Notation

I don't know how and where to start. I'll just think for a minute.
3. ### Prove Vector Quadruple Product with Levi-Civita/Index Notation

I found the mistake in my solution. I don't know if you're interested in knowing where the mistake is.

17. ### Special Relativity Problem -- Speeding through a red light to make it look green

I'm sorry but I disagree with this assesment in post #17 regarding this thread: The solutions given in post #6 and #9 are somewhat arbitrary and has some inconsistencies: I pointed these things out in post #8: It seems that no attention was paid to my misgivings and they only fell on deaf...
18. ### Help with a Gauss' law problem -- A long cylinder with a uniform charge density throughout

I only use Insert in MS Word to choose the shape that I want and I paste it on the document. Once you click on it the main menu Shape Format pops out and you can do almost anything the way you want it, to almost any measure that you like. It just needs familiarity and lots of practice. If you...
19. ### Help with a Gauss' law problem -- A long cylinder with a uniform charge density throughout

I don't understand this part of your last explanations: Why is the fraction ##~f~## not ##~f\neq a^2\Delta \phi/(πa^2)?## You used one that is half as small that I think it should be. But if one uses the formula for the area of a triangle ½×Base×Height, which I already mentioned in post #23...
20. ### Help with a Gauss' law problem -- A long cylinder with a uniform charge density throughout

In the second part of your arguments, the one with (math+physics), I don't get this: Isn't ##~\Delta \phi~## on the plane ⊥ to the ##~z~## axis subtending an ∠ with the ##~x~## and ##~y~## axes? And why do you have the factor 1/2 in the volume enclosed? For an infinitesimal volume, its simply...
21. ### Help with a Gauss' law problem -- A long cylinder with a uniform charge density throughout

I'm sorry but I already disagree with you right at the beginning of your arguments. $$\dots~{\rm {assumption~1:}} ~r = 0~ {\rm with} ~[E - ρr/(2ε_0)] \neq0~\Rightarrow~E\neq0~\dots$$ \dots~{\rm {assumption~2:}}~rE = 0~\Rightarrow~\begin{cases}\begin{align} & ~(i)~r = 0~{\rm...
22. ### Help with a Gauss' law problem -- A long cylinder with a uniform charge density throughout

@kuruman ... I know fully well what open surfaces and closed surfaces are and how they differ from lines. I also happen to know what coaxial cylinders are. I wasn't talking about reducing the ##~r~## of the imaginary Gaussian surface ##~\rm S~## to zero in post #7. I was referring to the range...
23. ### Help with a Gauss' law problem -- A long cylinder with a uniform charge density throughout

So, if one knows what happens in the neighborhood of the point in question, then one can make conclusions about the limit at exactly that point? Then, if one wants to talk next about the limit of the magnitude of the electric field ##~E~## at a point, one also has to examine the continuity of...
24. ### Help with a Gauss' law problem -- A long cylinder with a uniform charge density throughout

@Delta2 ... Thanks for your comments. But if ##~E=\rho r/2\epsilon_0~## for ##~r\neq 0~##, how did you get ##~\lim_{r\to 0}E=0~## for ##~r = 0~?~## Which expression for ##E~## did you use in evaluating the limit?
25. ### Help with a Gauss' law problem -- A long cylinder with a uniform charge density throughout

Could somebody familiar with the way mathematicians argue please take a look at this and make a comment? Thank you. I'm not a mathematician. What follows is about the electric field at the axis of a long uniformly charged right circular cylinder. Following his arguments in post #5, he obtained...
26. ### Help with a Gauss' law problem -- A long cylinder with a uniform charge density throughout

Okay, I was wrong. I'm sorry. I accept my mistake. But even without the mathematics, it is clear that ##E = 0## at the center of the uniformly charged cylinder because ##\vec E## run radially away from the axis so that pairs of them moving away opposite one another cancel out. I failed to see...
27. ### Help with a Gauss' law problem -- A long cylinder with a uniform charge density throughout

Given: ... a very long uniformly charged cylinder of radius ##R = 7.2~\rm cm = 0.072~\rm m~##... the volume charge density is ##ρ = 1264~\rm{nC} ⋅ \rm m^{-3} = 1.264~×~10^{-6}~\rm C ⋅ \rm m^{-3}~##... Unknown: ... the values of##~A~##and##~n~##for the electric field with magnitude##~E =...
28. ### Problem with differentiation

##f(t) = t^2\Rightarrow~##a distance function of time ##\Rightarrow~x(t) = At^2~\Leftarrow~A = 1~\rm m/s^2 = constant## ##\Rightarrow~dx/dt = 2At = v(t)~\dots## ##\Rightarrow~v(2~{\rm s}) = 2A(2~\rm s) = 2(1~{\rm m⋅s^{-2}})(2~\rm s) = 4~\rm m/s~\dots ## ##\Rightarrow~v(3~{\rm s}) = 2A(3~\rm s) =...
29. ### Problem with differentiation

Again, ##f(x) = x^2~\Rightarrow~df/dx = 2x## means that the rate of change of the function ##f(x)## with the independent variable ##x## is given by the function ##g(x) = 2x##. When ##x = 2##, the rate of change of the function ##f(x)## is given by ##g(2) = 2(2) = 4##. When ##x = 3##, the rate...
30. ### Problem with differentiation

Yes, its final value is 4.0 since ##f(x) = x^2~\Rightarrow~df/dx = 2x## and evaluating ##df/dx## at ##x_0 = 2## gives ##f'(x_0) = 2x_0 = 2(2) = 4 = f'(2)##.