The insulation property of air breaks down at $E = 3 \times 10^6 \ V/m$. The maximum charge that can be given to a sphere of diameter $5 \ m$ is approximately (in coulombs):

Four point positive charges of same magnitude $Q$ are placed at four corners of a rigid square frame in $xy$ plane as shown in the figure. The plane of the frame is perpendicular to the $z$-axis. If a negative point charge is placed at a distance $z$ away from the above frame $(z << L)$,then:

Infinite charges of magnitude $q$ each are placed at $x = 1, 2, 4, 8, ...$ meters on the $X$-axis. The value of the intensity of the electric field at the point $x = 0$ due to these charges will be:

The direction $(\theta)$ of the electric field $\vec{E}$ at point $P$ due to a uniformly charged finite rod is shown in the figure. Based on the geometry provided,determine the angle $\theta$.

The variation of electric field along the $Z$-axis due to a uniformly charged circular ring of radius '$a$' in the $XY$ plane is shown in the figure. The value of coordinate $M$ will be

The electric field lines on the left have twice the separation of those on the right as shown in the figure. If the magnitude of the electric field at $A$ is $40 \ Vm^{-1}$,what is the force on a $20 \ \mu C$ charge kept at $B$?