Two concentric conducting thin spherical shells of radii $a$ and $b\ (b > a)$ are given charges $Q$ and $ -2Q$ respectively. The electric field along a line passing through centre as a function of distance $(r)$ from centre is given by
Two concentric conducting thin spherical shells of radii $a$ and $b\ (b > a)$ are given charges $Q$ and $ -2Q$ respectively. The electric field along a line passing through centre as a function of distance $(r)$ from centre is given by
- A
- B
- C
- 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]
The region between two concentric spheres ofradii '$a$' and '$b$', respectively (see figure), have volume charge density $\rho = \frac{A}{r}$ where $A$ is a constant and $r$ is the distance from the centre. At the centre of the spheres is a point charge $Q$. The value of $A$ such that the electric field in the region between the spheres will be constant, is :
The region between two concentric spheres ofradii '$a$' and '$b$', respectively (see figure), have volume charge density $\rho = \frac{A}{r}$ where $A$ is a constant and $r$ is the distance from the centre. At the centre of the spheres is a point charge $Q$. The value of $A$ such that the electric field in the region between the spheres will be constant, is :
- [JEE MAIN 2016]
Two infinite planes each with uniform surface charge density $+\sigma$ are kept in such a way that the angle between them is $30^{\circ} .$ The electric field in the region shown between them is given by
Two infinite planes each with uniform surface charge density $+\sigma$ are kept in such a way that the angle between them is $30^{\circ} .$ The electric field in the region shown between them is given by
- [JEE MAIN 2020]
Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude $17.0\times 10^{-22}\; C/m^2$. What is $E$:
$(a)$ in the outer region of the first plate,
$(b)$ in the outer region of the second plate, and
$(c)$ between the plates?
Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude $17.0\times 10^{-22}\; C/m^2$. What is $E$:
$(a)$ in the outer region of the first plate,
$(b)$ in the outer region of the second plate, and
$(c)$ between the plates?
A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is $\left(\sigma / 2 \varepsilon_{0}\right) \hat{ n },$ where $\hat{ n }$ is the unit vector in the outward normal direction, and $\sigma$ is the surface charge density near the hole.
A hollow charged conductor has a tiny hole cut into its surface. Show that the electric field in the hole is $\left(\sigma / 2 \varepsilon_{0}\right) \hat{ n },$ where $\hat{ n }$ is the unit vector in the outward normal direction, and $\sigma$ is the surface charge density near the hole.