Recent content by Fanta

i got it. thanks

The problem doesn't state what exactly I'm trying to calculate. anyway, the integral would be \int_{0}^{2\pi} \int_{0}^{1}\int_{0}^{r} r^2 dz dr d\theta or \int_{0}^{2\pi} \int_{0}^{1}\int_{0}^{z} r^2 dr dz d\theta yes, i think i know what it looks like. Basically, since the limits are...

Just a question. Say you have a function, which in cylindrical coordinates it gives that \int\int\int \sqrt{x^2 + y^2} dx dy dz which is \int\int\int r^2 dr d/theta dz i want to find in cylindrical coordinates, in the area limited by the functions : x^2 + y^2 = z^2 z is greater or equal than...

so, outside of the sheets the electric field equals zero. Okay, got it. Thanks!

opposite.

Consider two infinite and plane uniform distributions of electric charge. One of the distributions is in the plane x = -a and the charge density sigma > 0. The other is in the plane x = a and the density is symmetric. I think we are. However i remember to have learned that when applying the...

between them? So how would you calculate the field outside of them? And why is there a field between the sheets, if the charge in the interior of the surface equals zero?

for example, the electric field between two symmetrically charged infinite planes would be given by : \oint E(r) \cdot n \cdot dS = \frac{Q_{interior}}{\epsilon_{0}} so, between both planes, E(r) = 0, and for r > a or r < a: E(r) = \frac{\sigma}{\epsilon_{0}} with sigma being the surface...

got it, thanks!

so, for example, for two infinite planes with symmetrical charges (if the charge is uniform throughout them) i can use a gaussian surface to determine the electric field?

When should I use one and when should I use the other? For example, suppose I have a rod of length 2L, with an edge on the point -L on the X axis and another on L. The rod is uniformly charged, with total charge Q>0. having that said, if i wanted to calculate the electric field in an arbitrary...

say we are given a subspace like this: Being W the subspace of R generated by (1,-2,3,-1), (1,1,-2,3) determine a basis and the dimension of the subspace. Won't the vectors given work as a basis, as long as they are linearly independent? If so, all we have to do is check for dependance, and if...

got it, thanks!

i see. So how would you calculate it then?

so, if I want to calculate the subspace spanned by A in: A = {(1,0,1) , (0,1,0)} in R^{3} c_{1}(1,0,1)+c_{2}(0,1,0) = (x,y,z) i can make a system: c_{1} = x c_{2} = y c_{1} = z from which I can conclude that x = z, and so, the subspace spanned will be the plane given by x =...