A fixed ring of radius $R$ is having uniformly distributed charge $Q$ over its circumference. A charge $q$ of opposite nature and mass $m$ is kept on its axis at a distance $\mathrm{x}\ll R$ from the centre of ring. If charge is released from rest then minimum time after which it will pass through centre of the ring will be (Effect of gravity is considered to be negligible) $\left(k=\frac{1}{4\pi {\epsilon }_0}\right)$

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 $P\left(a, a, a\right).$

A semi-infinite wire of uniform linear charge density $\lambda$ is placed as shown in figure. The conical surface is of radius $R$ and height $h.$The electric flux through the curved surface of the cone is

Three point charges $+Q,-Q$ and $+2Q$ are placed at the vertices of an isosceles right angled triangle as shown in figure. The magnitude of electric field intensity produced by these charges at the middle point of hypotenuse is