- #1
toomuchfries
- 3
- 0
Homework Statement
Find an expression for the magnetic field of a hollow finite solenoid carrying uniform current with n turns (there is no top or bottom surfaces and the turns a very closely winded) at a point arbitrary P both inside and outside. Let's just say windings around a hollow pvc pipe.
Homework Equations
I can use either biot savarts law and/or magnetic vector potential for surface currents. I'll use griffiths notation 3rd edition equations 5.39 and 5.64 respectively.
The Attempt at a Solution
I'll attempt this in cylinderical coordinates. Since the current is uniform. I'll use the
[itex]\vec{A}\left(\vec{r}\right)=\frac{1}{4\pi}\int\frac{\vec{K\left(r'\right)}}{\tau}da'[/itex]
Current density [itex]\vec{K}[/itex] is in the [itex]\hat{\phi}[/itex]
so [itex]\vec{K}=\frac{nI}{z'}\hat{\phi}[/itex] ? Since current is uniform.
[itex]\tau=\left|r-r'\right|[/itex]
[itex]r=s\hat{s}+s\phi\hat{\phi}+z\hat{z}[/itex]
[itex]r'=s\hat{s}?[/itex]
[itex]da'=sd\phi'dz'[/itex]
Where the limits of phi' is 0->2*pi and z' is 0 -> L (length of cylinder)