During lightning,a current pulse,as shown in the figure,flows from a cloud at a height of $1.5 \ km$ to the ground. If the breakdown electric field of humid air is about $400 \ kVm^{-1}$,the energy released during lightning would be (in units of $10^9 \ J$):

Consider a system of three charges $\frac{q}{3}, \frac{q}{3}$ and $-\frac{2q}{3}$ placed at points $A, B$ and $C$,respectively,as shown in the figure. Take $O$ to be the centre of the circle of radius $R$ and angle $\angle CAB = 60^{\circ}$.

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:

In $1959$,Lyttleton and Bondi suggested that the expansion of the Universe could be explained if matter carried a net charge. Suppose that the Universe is made up of hydrogen atoms with a number density $N$,which is maintained constant. Let the charge on the proton be: $e_p = -(1 + y)e$,where $e$ is the electronic charge.
$(a)$ Find the critical value of $y$ such that expansion may start.
$(b)$ Show that the velocity of expansion is proportional to the distance from the centre.

The diagram shows three infinitely long uniform line charges placed on the $X, Y$ and $Z$ axes with linear charge densities $2\lambda, 3\lambda$ and $\lambda$ respectively. The work done by an external agent in moving a unit positive charge from $(1, 1, 1)$ to $(0, 1, 1)$ is equal to:

Two identical small spheres carry charges $Q_1$ and $Q_2$ $(Q_1 >> Q_2)$. The force between them is $F_1$. The spheres are brought into contact and then placed at the same distance. The new force between them is $F_2$. Then $F_1/F_2$ will be: