Recent content by kacete

Check the quantum theory of paramagnetism about 'magnetism and angular momentum'.

Thank you, I will try that!

Is there no easier way of solving this rather than integrating the following? \int^{10^{-6}}_{0} \int^{ \pi }_{0} \int^{2 \pi }_{0} \left( \frac{100(rsin \theta sin \phi +8)}{(rcos \ntheta +1)^{2} +1} - \frac{100(3(rcos \theta +1)^{2}-1)(rsin \theta cos \phi +5)^{2}(r sin \theta sin \phi...

Of course, but I have to switch the divergence calculated before to spherical coordinates too, right?

\frac{\partial}{\partial z}\left( - \frac{100x^2 y z}{(z^2+1)^2}\right)=\frac{100(3z^{2}-1)x^{2}y}{(z^{2}+1)^{3}} You're right, I corrected it. (plus i had a typo in my problem, the last one - in direction of z - is negative). I thought that too. But I don't know how to integrate to the whole...

No, since it does not contain an y variable, the derivate in order of y is 0. I replaced the variables with the coordinates for the center of the sphere to find the value in that region.

I got the following result: \vec{\nabla}.\vec{D}=\frac{100y}{z^{2}+1}-\frac{400x^{2}y^{2}z}{(z^{2}+1)^{3}} Then I replaced with the coordinates and got: \vec{\nabla}.\vec{D}=-79600 Calculated the sphere volume: V=\frac{4\pi r^{3}}{3} And multiplied both: Q=-3.334.10^{-13} It's close, but...

Homework Statement Given the Electric flux density of \vec{D}=\frac{100xy}{z^{2}+1}\vec{u_{x}}+\frac{50x^{2}}{z^{2}+1}\vec{u_{y}}+\frac{100x^{2}yz}{(z^{2}+1)^{2}}\vec{u_{x}} C/m^{2} find the total charge inside a tiny sphere with a radius of r=1\mu m centered in c(5,8,1).Homework Equations...

Can't believe it was that simple. I'm embarrassed. Thank you!

Homework Statement Given the Electric field \vec{E}=z\vec{u_{x}}-3y^{2}\vec{u_{y}}+x\vec{u_{z}} V/m find the necessary Work to move a charge Q=7\mu C along an incremental path of 1mm distance in the direction of 2\vec{u_{x}}-6\vec{u_{y}}-3\vec{u_{z}} which locates in P(1,2,3) Homework...

Probably the second. Are you supposed to take the negative of the integral out?

I managed to solve to the right solution, except that I get a negative value: -106 instead of 106. What did I do wrong? Or is this expected?

Right! I understand it now. Yes, it's easier than to parametrize the line. I didn't think of that, but it makes sense. Thank you! I will try it.

Like this? V_{PQ}=-\int^{P}_{Q}\vec{E}d\vec{L}=-(\int^{2}_{1}E\vec{u_{x}}dL\vec{u_{x}} + \int^{1}_{-1}E\vec{u_{y}}dL\vec{u_{y}} + \int^{3}_{0}E\vec{u_{y}}dL\vec{u_{y}})

I believe I understand now. Thank you very much for your help, I will try that.