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 $10^9 \ J$):

The time period of a block of mass $m$ suspended from the upper plate of a parallel plate capacitor by a spring of stiffness $k$ is $T$ when the block is uncharged. If a charge $q$ is given to the block,what will be the new time period of oscillation?

Two charges each of magnitude $Q$ are fixed at a distance of $2a$ apart. $A$ third charge ($-q$ of mass $m$) is placed at the midpoint of the two charges. If the $-q$ charge is slightly displaced perpendicular to the line joining the charges,find its time period.

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:

An infinite plane sheet of charge having uniform surface charge density $+\sigma_s \text{ C/m}^2$ is placed on the $x-y$ plane. Another infinitely long line charge having uniform linear charge density $+\lambda_e \text{ C/m}$ is placed at the $z=4 \text{ m}$ plane and is parallel to the $y$-axis. If the magnitude values satisfy $|\sigma_s| = 2|\lambda_e|$,then at the point $(0, 0, 2)$,the ratio of the magnitudes of the electric field values due to the sheet charge to that of the line charge is $\pi \sqrt{n} : 1$. The value of $n$ is:

$A$ charged particle of charge $Q$ is held fixed and another charged particle of mass $m$ and charge $q$ (of the same sign) is released from a distance $r$. The impulse of the force exerted by the external agent on the fixed charge by the time the distance between $Q$ and $q$ becomes $2r$ is: