A long charged cylinder of linear charged density λ is surrounded by a hollow co-axial conducting c

English

Gujarati

Hindi

1. Electric Charges and Fields

medium

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?

Option A

Option B

Option C

Option D

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

Standard 12

Physics

Share

Similar Questions

If a small sphere of mass $m$ and charge $q$ is hung from a silk thread at an angle $\theta$ with the surface of a vertical charged conducting plate, then for equilibrium of sphere, the surface charge density of the plate is

medium

An isolated sphere of radius $R$ contains uniform volume distribution of positive charge. Which of the curve shown below, correctly illustrates the dependence of the magnitude of the electric field of the sphere as a function of the distance $r$ from its centre?

normal

(KVPY-2011)

A spherical conductor of radius $10\, cm$ has a charge of $3.2 \times 10^{-7} \,C$ distributed uniformly. What is the magnitude of electric field at a point $15 \,cm$ from the centre of the sphere?

$\left(\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} Nm ^{2} / C ^{2}\right)$

medium

(NEET-2020)

An infinite plane sheet of charge having uniform surface charge density $+\sigma_5 \mathrm{C} / \mathrm{m}^2$ is placed on $\mathrm{x}-\mathrm{y}$ plane. Another infinitely long line charge having uniform linear charge density $+\lambda_e \mathrm{C} / \mathrm{m}$ is placed at $z=4 \mathrm{~m}$ plane and parallel to $y$-axis. If the magnitude values $\left|\sigma_s\right|=2\left|\lambda_{\mathrm{e}}\right|$ then at point $(0,0,2)$, the ratio of magnitudes of electric field values due to sheet charge to that of line charge is $\pi \sqrt{\mathrm{n}}: 1$. The value of $n$ is

hard

(JEE MAIN-2024)

Obtain the expression of electric field by ……

$(i)$ infinite size and with uniform charge distribution.

$(ii)$ thin spherical shell with uniform charge distribution at a point outside it.

$(iii)$ thin spherical shell with uniform charge distribution at a point inside it.

hard