A sphere of radius $R$ and charge $Q$ is placed inside a concentric imaginary sphere of radius $2R$. The flux associated with the imaginary sphere is

A charge $Q$ is enclosed by a Gaussian spherical surface of radius $R$. If the radius is doubled, then the outward electric flux will

A long cylindrical volume contains a uniformly distributed charge of density $\rho$. The radius of cylindrical volume is $R$. A charge particle $(q)$ revolves around the cylinder in a circular path. The kinetic of the particle is

Gauss’s law is true only if force due to a charge varies as

If atmospheric electric field is approximately $150 \,volt / m$ and radius of the earth is $6400 \,km$, then the total charge on the earth's surface is .......... coulomb

A disk of radius $a / 4$ having a uniformly distributed charge $6 \mathrm{C}$ is placed in the $x-y$ plane with its centre at $(-a / 2,0,0)$. A rod of length $a$ carrying a uniformly distributed charge $8 \mathrm{C}$ is placed on the $x$-axis from $x=a / 4$ to $x=5 a / 4$. Two point charges $-7 \mathrm{C}$ and $3 \mathrm{C}$ are placed at $(a / 4,-a / 4,0)$ and $(-3 a / 4,3 a / 4,0)$, respectively. Consider a cubical surface formed by six surfaces $x= \pm a / 2, y= \pm a / 2$, $z= \pm a / 2$. The electric flux through this cubical surface is