રેખીય વિદ્યુતભાર ઘનતા $\lambda$ ધરાવતો એક લાંબો નળાકાર એક પોલા, સમઅક્ષીય, સુવાહક નળાકાર વડે ઘેરાયેલ છે. બે નળાકારની વચ્ચેના અવકાશમાં વિદ્યુતક્ષેત્ર કેટલું હશે?

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 $\frac{\lambda}{2 \pi \epsilon_{0} d}$