I have a stationary electric current like this: [itex]\vec{I}=I_0\vec{e_z}[/itex] and I have to calculate the electric and magnetic fields from an inertial frame that is moving with velocity [itex]\vec{v}=v\vec{e_z}[/itex].
First I calculate the vector potential from a rest frame (and then I'll use Maxwell equations to get B and Lorentz transformation for E' and B') and I use cilindrical coordinates, so I get:
[itex]\vec{A}= \frac{\mu _0}{4\pi}∫\frac{dz}{\sqrt{r^2+z^2}}[/itex]
but if I calculate this between -infinity and infinity the integral diverges.
Can this integral be solved? Or, is there an easier way to solve the problem?
Thank you.
First I calculate the vector potential from a rest frame (and then I'll use Maxwell equations to get B and Lorentz transformation for E' and B') and I use cilindrical coordinates, so I get:
[itex]\vec{A}= \frac{\mu _0}{4\pi}∫\frac{dz}{\sqrt{r^2+z^2}}[/itex]
but if I calculate this between -infinity and infinity the integral diverges.
Can this integral be solved? Or, is there an easier way to solve the problem?
Thank you.