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 |
$P \rightarrow 5 ; Q \rightarrow 3,4 ; R \rightarrow 1 ; S \rightarrow 2$
$P \rightarrow 5 ; Q \rightarrow 3 ; R \rightarrow 1,4 ; S \rightarrow 2$
$P \rightarrow 5 ; Q \rightarrow 3 ; R \rightarrow 1,2 ; S \rightarrow 4$
$P \rightarrow 4 ; Q \rightarrow 2,3 ; R \rightarrow 1 ; S \rightarrow 5$
A conducting sphere of radius $R = 20$ $cm$ is given a charge $Q = 16\,\mu C$. What is $\overrightarrow E $ at centre
Two concentric conducting thin spherical shells $A$ and $B$ having radii ${r_A}$ and ${r_B}$ (${r_B} > {r_A})$ are charged to ${Q_A}$ and $ - {Q_B}$$(|{Q_B}|\, > \,|{Q_A}|)$. The electrical field along a line, (passing through the centre) is
A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is
Explain by graph how the electric field by thin spherical shell depends on the distance of point from centre.
Two parallel infinite line charges with linear charge densities $+\lambda\; \mathrm{C} / \mathrm{m}$ and $-\lambda\; \mathrm{C} / \mathrm{m}$ are placed at a distance of $2 \mathrm{R}$ in free space. What is the electric field mid-way between the two line charges?