- #1
Edwardo_Elric
- 101
- 0
Homework Statement
i was deriving an infinite line of charge formula by coloumb's law:
so i got stuck with this integral (since it is in the maths forum)
[tex] \vec{E}_{\rho} = \int_{-\infty}^{\infty} \frac{\rho_L \rho dz}{4\pi\epsilon_o ({\rho}^2 + z^2)^{\frac{3}{2}}} [/tex]
Homework Equations
where
[tex]{\rho}_L = [/tex] linear charge density
[tex]{\rho} = [/tex] direction perpendicular to z axis in cylindrical coordinates
The Attempt at a Solution
so when integrating (using trigo substitution):
[tex] \vec{E}_{\rho} = \frac{\rho_L\rho}{4\pi\epsilon_o} (\frac{1}{{\rho}^2} \frac{z}{p^2 + z^2})_{-\infty}^{\infty} [/tex]
this is where i got stuck
no matter how i use lhopitals rule in this equation:
\lim_{z \infty} \frac{z}{({\rho}^2 + z^2)^{\frac{1}{2}}
it keeps going back
because the infinite is supposed to add to equate to 2
the answer which is
[tex] \vec{E}_{\rho} = \frac{\rho_L}{2\pi\epsilon_o\rho}[/tex]
Last edited: