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

$\mathrm{C}_1$ 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 :

An electric line of force in the $xy$ plane is given by equation ${x^2} + {y^2} = 1$. A particle with unit positive charge, initially at rest at the point $x = 1,\;y = 0$ in the $xy$ plane

When the electric flux associated with closed surface becomes positive, zero or negative ?

Gauss’s law should be invalid if

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