A long charged cylinder of linear charged density $\lambda$ is surrounded by a hollow co-axial conducting cylinder. What is the electric field in the space between the two cylinders?
A long charged cylinder of linear charged density $\lambda$ is surrounded by a hollow co-axial conducting cylinder. What is the electric field in the space between the two cylinders?
Charge density of the long charged cylinder of length $L$ and radius $r$ is $\lambda$.
Another cylinder of same length surrounds the pervious cylinder.
The radius of this cylinder is $R$. Let $E$ be the electric field produced in the space between the two cylinders.
Electric flux through the Gaussian surface is given by Gauss's theorem as,
$\phi=E(2 \pi d) L$
Where, $d=$ Distance of a point from the common axis of the cylinders Let
$q$ be the total charge on the cylinder.
It can be written as $\therefore \phi=E(2 \pi d L)=\frac{q}{\epsilon_{0}}$
Where, $q=$ Charge on the inner sphere of the outer cylinder
$\varepsilon_{0}=$ Permittivity of free space $E(2 \pi d L)=\frac{\lambda L}{\epsilon_{0}}$
$E=\frac{\lambda}{2 \pi \epsilon_{0} d}$
Therefore, the electric field in the space between the two cylinders is $\frac{\lambda}{2 \pi \epsilon_{0} d}$
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