The dimension of $\frac{1}{2} \varepsilon_0 E^2$,where $\varepsilon_0$ is the permittivity of free space and $E$ is the electric field,is:

Answer the following:
$(a)$ The top of the atmosphere is at about $400 \; kV$ with respect to the surface of the earth,corresponding to an electric field that decreases with altitude. Near the surface of the earth,the field is about $100 \; Vm^{-1}$. Why then do we not get an electric shock as we step out of our house into the open? (Assume the house to be a steel cage so there is no field inside!)
$(b)$ $A$ man fixes outside his house one evening a two-metre-high insulating slab carrying on its top a large aluminium sheet of area $1 \; m^2$. Will he get an electric shock if he touches the metal sheet next morning?
$(c)$ The discharging current in the atmosphere due to the small conductivity of air is known to be $1800 \; A$ on an average over the globe. Why then does the atmosphere not discharge itself completely in due course and become electrically neutral? In other words,what keeps the atmosphere charged?
$(d)$ What are the forms of energy into which the electrical energy of the atmosphere is dissipated during lightning?

Four point charges,each of $+q$,are rigidly fixed at the four corners of a square planar soap film of side $a$. The surface tension of the soap film is $\gamma$. The system of charges and the planar film are in equilibrium,and $a = k \left[ \frac{q^2}{\gamma} \right]^{1/N}$,where $k$ is a constant. Then $N$ is:

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-$II$
$P$. $E$ is independent of $d$	$1$. $A$ point charge $Q$ at the origin
$Q$. $E \propto \frac{1}{d}$	$2$. $A$ small dipole with point charges $Q$ at $(0, 0, l)$ and $-Q$ at $(0, 0, -l)$. Take $2l \ll d$.
$R$. $E \propto \frac{1}{d^2}$	$3$. An infinite line charge coincident with the $x$-axis,with uniform linear charge density $\lambda$
$S$. $E \propto \frac{1}{d^3}$	$4$. 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 $2l \ll d$
	$5$. Infinite plane with uniform surface charge density

An ellipsoidal cavity is carved within a perfect conductor. $A$ positive charge $q$ is placed at the centre of the cavity. The points $A$ and $B$ are on the cavity surface as shown in the figure. Then

$A$ cube of side $b$ has a charge $q$ at each of its vertices. The electric field due to this charge distribution at the centre of this cube will be