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

On a non-conducting ring of radius $R,+q$ and $-q$ charges are uniformly distributed in two halves as shown in figure. The electric field intensity on its axis at a distance $d$ from its centre is given by $\overrightarrow{E}$, then

Two point charges $A$ and $B$ are placed on $X$-axis. Considering electric field $E$ is positive if directed in positive $X$-direction. Variation of electric field strength with distance $x$ is shown in figure for $x$ lying between the charges. Then the nature of charges $A$ and $B$ are respectively

A non-conducting square plate of side length $2a$ is uniformly charged with charge $Q$ and a point charge $q$ is placed at perpendicular distance $a$ as shown in figure. The electric force on the point charge due to plate is

An annular disc of inner radius $R$ and outer radius $2R$ has uniformly distributed charge $Q.$ Electric field strength at point $P$ is