Two point charges placed at a distance $r$ in air experience a certain force. Then the distance at which they will experience the same force in a medium of dielectric constant $K$ is

Electric flux through surface $s_1$

If $\vec E = \frac{{{E_0}x}}{a}\hat i\,\left( {x - mt} \right)$ then flux through the shaded area of a cube is

A capacitor of capacitance $C_0$ is charged to a potential $V_0$ and is connected with another capacitor of capacitance $C$ as shown. After closing the switch $S$, the common potential across the two capacitors becomes $V$. The capacitance $C$ is given by

A parallel plate capacitor with air between the plates has a capacitance of $9\, pF$. The separation between its plates is $'d'$. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant $K_1=3$ and thickness $\frac{d}{3}$ while the other one has dielectric constant $K_2 = 6$ and thickness $\frac{2d}{3}$ . Capacitance of the capacitor is now.........$pF$

Two spherical conductors $A$ and $B$ of radii $1\, mm$ and $2\, mm$ are separated by  a distance of $5\, cm$ and are uniformly charged. If the spheres are connected by a  conducting wire then in equilibrium condition, the ratio of the magnitude of the electric  fields at the surfaces of spheres $A$ and $B$ is-