What is the net flux of the uniform electric field of $E =3 \times 10^{3} i\; N / C $ through a cube of side $20\; cm$ oriented so that its faces are parallel to the coordinate planes?

Three charges $q_1 = 1\,\mu c, q_2 = 2\,\mu c$ and $q_3 = -3\,\mu c$ and four surfaces $S_1, S_2 ,S_3$ and $S_4$ are shown in figure. The flux emerging through surface $S_2$ in $N-m^2/C$ is

A charge $Q$ is situated at the comer of a cube, the electric flux passed through all the six faces of the cube is

An arbitrary surface encloses a dipole. What is the electric flux through this surface ?

Draw electric field lines of simple charge distribution.

A charged shell of radius $R$ carries a total charge $Q$. Given $\Phi$ as the flux of electric field through a closed cylindrical surface of height $h$, radius $r$ and with its center same as that of the shell. Here, center of the cylinder is a point on the axis of the cylinder which is equidistant from its top and bottom surfaces. Which of the following option(s) is/are correct ? $\epsilon_0$ is the permittivity of free space]

$(1)$ If $h >2 R$ and $r > R$ then $\Phi=\frac{ Q }{\epsilon_0}$

$(2)$ If $h <\frac{8 R }{5}$ and $r =\frac{3 R }{5}$ then $\Phi=0$

$(3)$ If $h >2 R$ and $r =\frac{4 K }{5}$ then $\Phi=\frac{ Q }{5 \epsilon_0}$

$(4)$ If $h >2 R$ and $r =\frac{3 K }{5}$ then $\Phi=\frac{ Q }{5 \epsilon_0}$