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 |
$P \rightarrow 5 ; Q \rightarrow 3,4 ; R \rightarrow 1 ; S \rightarrow 2$
$P \rightarrow 5 ; Q \rightarrow 3 ; R \rightarrow 1,4 ; S \rightarrow 2$
$P \rightarrow 5 ; Q \rightarrow 3 ; R \rightarrow 1,2 ; S \rightarrow 4$
$P \rightarrow 4 ; Q \rightarrow 2,3 ; R \rightarrow 1 ; S \rightarrow 5$
Obtain the formula for the electric field due to a long thin wire of uniform linear charge density $E$ without using Gauss’s law.
The electric field at a distance $\frac{3R}{2}$ from the centre of a charged conducting spherical shell of radius $R$ is $E.$ The electric field at a distance $\frac{R}{2}$ from the centre of the sphere is
A charge $Q$ is uniformly distributed over a large square plate of copper. The electric field at a point very close to the centre of the plane is $10\, V/m$. If the copper plate is replaced by a plastic plate of the same geometrical dimensions and carrying the same charge $Q$ uniformly distributed, then the electric field at the point $P$ will be......$V/m$
Consider an atom with atomic number $Z$ as consisting of a positive point charge at the centre and surrounded by a distribution of negative electricity uniformly distributed within a sphere of radius $R$. The electric field at a point inside the atom at a distance $r$ from the centre is
Let $P\left( r \right) = \frac{Q}{{\pi {R^4}}}r$ be the charge density distribution for a solid sphere of radius $R$ and total charge $Q$. For a point $P$ inside the sphere at distance $r_1$ from the centre of the sphere, the magnitude of electric field is