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 $\frac{\lambda}{2 \pi \epsilon_{0} d}$
Similar Questions
The electric field $E$ is measured at a point $P (0,0, d )$ generated due to various charge distributions and the dependence of $E$ on $d$ is found to be different for different charge distributions. List-$I$ contains different relations between $E$ and $d$. List-$II$ describes different electric charge distributions, along with their locations. Match the functions in List-$I$ with the related charge distributions in List-$II$.
List-$I$
List-$II$
$E$ is independent of $d$
A point charge $Q$ at the origin
$E \propto \frac{1}{d}$
A small dipole with point charges $Q$ at $(0,0, l)$ and $- Q$ at $(0,0,-l)$. Take $2 l \ll d$.
$E \propto \frac{1}{d^2}$
An infinite line charge coincident with the x-axis, with uniform linear charge density $\lambda$
$E \propto \frac{1}{d^3}$
Two infinite wires carrying uniform linear charge density parallel to the $x$-axis. The one along ( $y=0$, $z =l$ ) has a charge density $+\lambda$ and the one along $( y =0, z =-l)$ has a charge density $-\lambda$. Take $2 l \ll d$
plane with uniform surface charge density
The electric field $E$ is measured at a point $P (0,0, d )$ generated due to various charge distributions and the dependence of $E$ on $d$ is found to be different for different charge distributions. List-$I$ contains different relations between $E$ and $d$. List-$II$ describes different electric charge distributions, along with their locations. Match the functions in List-$I$ with the related charge distributions in List-$II$.
| List-$I$ | List-$II$ |
| $E$ is independent of $d$ | A point charge $Q$ at the origin |
| $E \propto \frac{1}{d}$ | A small dipole with point charges $Q$ at $(0,0, l)$ and $- Q$ at $(0,0,-l)$. Take $2 l \ll d$. |
| $E \propto \frac{1}{d^2}$ | An infinite line charge coincident with the x-axis, with uniform linear charge density $\lambda$ |
| $E \propto \frac{1}{d^3}$ | Two infinite wires carrying uniform linear charge density parallel to the $x$-axis. The one along ( $y=0$, $z =l$ ) has a charge density $+\lambda$ and the one along $( y =0, z =-l)$ has a charge density $-\lambda$. Take $2 l \ll d$ |
| plane with uniform surface charge density |
- [IIT 2018]
A hollow metal sphere of radius $R$ is uniformly charged. The electric field due to the sphere at a distance r from the centre
A hollow metal sphere of radius $R$ is uniformly charged. The electric field due to the sphere at a distance r from the centre
- [NEET 2019]
Consider a metal sphere of radius $R$ that is cut in two parts along a plane whose minimum distance from the sphere's centre is $h$. Sphere is uniformly charged by a total electric charge $Q$. The minimum force necessary to hold the two parts of the sphere together, is
Consider a metal sphere of radius $R$ that is cut in two parts along a plane whose minimum distance from the sphere's centre is $h$. Sphere is uniformly charged by a total electric charge $Q$. The minimum force necessary to hold the two parts of the sphere together, is
Two infinite sheets of uniform charge density $+\sigma$ and $-\sigma $ are parallel to each other as shown in the figure. Electric field at the
Two infinite sheets of uniform charge density $+\sigma$ and $-\sigma $ are parallel to each other as shown in the figure. Electric field at the
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?
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?
- [KVPY 2011]