The cylindrical chamber electric field

[jhon]

In the cylindrical chamber, the voltage is applied to a very thin wire, a few mills of an inch in diameter, stretched axially at the center of the cylinder. The cylinder wall is usually grounded. The electric field is, in this case,

E=\frac{V_{0}}{Ln(b/a)r}
where
a = radius of the central wire
b = radius of the counter
r = distance from the center of the counter
sea figure
http://img412.imageshack.us/img412/3176/84851789.jpg
how i can prove this equation

 

[stevenb]

The electric field as a function of charge is easily derived with Gauss' law. Then charge and voltage can be related through capacitance. Capacitance of a cylyndrical capacitor is well known and the derivation can quickly found in any EM book or with Google.

 

[jhon]

thanks