The electric field in a region is given $\vec E = a\hat i + b\hat j$ . Here $a$ and $b$ are constants. Find the net flux passing through a square area of side $l$ parallel to $y-z$ plane

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 $\Phi=\frac{ Q }{5 \epsilon_0}$

The spatial distribution of the electric field due to two charges $(A,\,B)$ is shown in figure. Which one of the following statements is correct ?

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

The electric field in a region is radially outward with magnitude $E = A{\gamma _0}$. The charge contained in a sphere of radius ${\gamma _0}$ centered at the origin is

The given figure gives electric lines of force due to two charges $q_1$ and $q_2$. What are the signs of the two charges?