The electric field inside a sphere which carries a charge density proportional to the distance from the centre $\rho =\alpha r$ (where, $\alpha$ is constant) is,

Due to charge inside a cube, the electric field is, $E_{\mathrm{x}}=600x^{\frac{1}{2}}$, $E_y=0$, $E_z=0$. The charge inside the cube is (approximately),

A charged particle $q$ is placed at the centre $O$ of cube of length $L\left(ABCDEFGH\right)$. Another same charge $q$ is placed at a distance $L$ from $O$. Then, the electric flux through $ABCD$ is,

An infinite uniformly charged sheet with surface charge density $\sigma$ cuts through a spherical gaussian surface of radius $R$ at a distance $x$ from its center as shown in the figure. The electric flux $\varphi$ through the gaussian surface is,

A disk of radius $\frac{a}{4}$ having a uniformly distributed charge $6 \mathrm{C}$ is placed in the $x-y$ plane with its centre at $\left(-\frac{a}{2}, 0, 0\right)$. A rod of length $a$ carrying a uniformly distributed charge $8 \mathrm{C}$ is placed on the $x$-axis from $x=\frac{a}{4}$ to $x=\frac{5a}{4}$. Two point charges $-7 \mathrm{C}$ and $3 \mathrm{C}$ are placed at $\left(\frac{a}{4},-\frac{a}{4}, 0\right)$ and $\left(-\frac{3a}{4},\frac{3a}{4}, 0\right)$, respectively. Consider a cubical surface formed by six surfaces, $x=\pm \frac{a}{2}, y=\pm \frac{a}{2}, z=\pm \frac{a}{2}$. The electric flux through this cubical surface is,