Four closed surfaces and corresponding charge distributions are shown below

Let the respective electric fluxes through the surfaces be ${\phi _1},{\phi _2},{\phi _3}$ and ${\phi _4}$ . Then

$\mathrm{C}_1$ and $\mathrm{C}_2$ are two hollow concentric cubes enclosing charges $2 Q$ and $3 Q$ respectively as shown in figure. The ratio of electric flux passing through $\mathrm{C}_1$ and $\mathrm{C}_2$ is :

A cylinder of radius $R$ and length $L$ is placed in a uniform electric field $E$ parallel to the cylinder axis. The total flux for the surface of the cylinder is given by

The circular wire in figure below encircles solenoid in which the magnetic flux is increasing at a constant rate out of the plane of the page. The clockwise emf around the circular loop is $\varepsilon_{0}$. By definition a voltammeter measures the voltage difference between the two points given by $V_{b}-V_{a}=-\int \limits_{a}^{b} E \cdot d s$ We assume that $a$ and $b$ are infinitesimally close to each other. The values of $V_{b}-V_{a}$ along the path $1$ and $V_{a}-V_{b}$ along the path $2$ , respectively are

Electric lines of force about negative point charge are

An infinitely long uniform line charge distribution of charge per unit length $\lambda$ lies parallel to the $y$-axis in the $y-z$ plane at $z=\frac{\sqrt{3}}{2} a$ (see figure). If the magnitude of the flux of the electric field through the rectangular surface $A B C D$ lying in the $x-y$ plane with its center at the origin is $\frac{\lambda L }{ n \varepsilon_0}\left(\varepsilon_0=\right.$ permittivity of free space $)$, then the value of $n$ is