A point charge of $+\,12 \,\mu C$ is at a distance $6 \,cm$ vertically above the centre of a square of side $12\, cm$ as shown in figure. The magnitude of the electric flux through the square will be ……. $\times 10^{3} \,Nm ^{2} / C$

The flat base of a hemisphere of radius $a$ with no charge inside it lies in a horizontal plane. A uniform electric field $\vec E$ is applied at an angle $\frac {\pi }{4}$ with the vertical direction. The electric flux through the curved surface of the hemisphere is

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

How much electric flux will come out through a surface $S = 10\hat j$ kept in an electrostatic field $\vec E = 2\hat i + 4\hat j + 7\hat k$………$units$

An electron revolves around an infinite cylindrical wire having uniform linear change density $2 \times 10^{-8}\,Cm ^{-1}$ in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is revolving is $………\times 10^6\,ms ^{-1}$. Given mass of electron $=9 \times 10^{-31}\,kg$