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...
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...
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...
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 =...