Consider an electric field $\overrightarrow{E}=E_0\hat{x}$, where $E_0$ is a constant. The flux through the shaded area (as shown in the figure) due to this field is $n{E}_0{a}^2.$ The value of $n$ 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 $(–\frac{a}{2}, 0, 0).$A rod of length a carrying a uniformly distributed charge $8\mathrm{C}$ is placed on the x-axis from $x=\frac{a}{4}\text{ to} x=\frac{5a}{4}$ Two point charges $-7\mathrm{C}$ and $3\mathrm{C}$ are placed at $(\frac{a}{4}, –\frac{a}{4}, 0)$ and $(–\frac{3a}{4}, \frac{3a}{4}, 0),$ respectively. Consider a cubical surface formed by six surfaces $x=\pm \frac{a}{4}, y=\pm \frac{a}{4}, z=\pm \frac{a}{4}.$ The electric flux through this cubical surface is 

A point charge $q$ is placed at a normal distance $d$ from one edge of a semi-infinite large plate as shown in figure. Find net electric flux passing through this plate.

A solid non-conducting uniformly charged sphere having charge $Q$ and radius $R$ is placed at a separation of $2R$ from the centre of ring as shown in figure (centre of sphere lies on the axis of ring). Force on sphere due to ring is (Charge on ring is $2Q$ and its radius is $R$)

A short dipole of dipole moment $\overrightarrow{P}$ is placed along $x$-axis at a distance $d$ from a long wire having uniform linear charge density $+\lambda$ (wire is along $Y$ axis) as shown. Find minimum work required to align this dipole along $y$ axis (so that dipole moment $\overrightarrow{P}$ is along $+y$ direction)

Four point charges are fixed at the corners of a square of side length $a.$ (in horizontal $x-y$ plane). A positive charge $q_0$ is placed at a distance a from centre of square perpendicular to the plane of square. If point charge $q_0$ is in equilibrium then its mass $m$ is $\left(a=\sqrt{\frac{3}{2}}m\right).$

An infinitely large plate of width $b$ is placed in horizontal $x-y$ plane. A point charge $q_0$ is placed symmetrically at a distance of $\frac{b}{2}$ perpendicular to plane of this plate as shown. Find electric flux passing through this plate.

Three infinitely long wires having uniform linear charge density $\lambda$ are placed along $x, y$, and $z$-axis respectively. Find electric field at point $P\left(a, a, a\right).$