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रैखिक आवेश घनत्व $\lambda$ वाला एक लंबा आवेशित बेलन एक खोखले समाक्षीय चालक बेलन द्वारा घिरा है। दोनों बेलनों के बीच के स्थान में विध्यूत क्षेत्र कितना है?
Solution
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 $\frac{\lambda}{2 \pi \epsilon_{0} d}$
