Find the value of $q$ so that the net electrostatic force on the $10 \mu C$ charge placed at a vertex of the square is zero. The charges are arranged as shown in the figure.

Two balls with equal charges are in a vessel with ice at $-10^{\circ} C$ at a distance of $25 \ cm$ from each other. On forming water at $0^{\circ} C$,the balls are brought nearer to $5 \ cm$ for the interaction between them to be same. If the dielectric constant of water at $0^{\circ} C$ is $80$,the dielectric constant of ice at $-10^{\circ} C$ is:

Two identical conducting spheres with negligible volume have $2.1 \, nC$ and $-0.1 \, nC$ charges,respectively. They are brought into contact and then separated by a distance of $0.5 \, m$. The electrostatic force acting between the spheres is $.......... \times 10^{-9} \, N$. [Given: $\frac{1}{4 \pi \varepsilon_{0}} = 9 \times 10^{9} \, N \cdot m^{2}/C^{2}$]

$A$ small uncharged conducting sphere is placed in contact with an identical sphere having a charge of $4 \times 10^{-8} \text{ C}$. They are then separated to a distance such that the force of repulsion between them is $9 \times 10^{-3} \text{ N}$. The distance between them is (Take $\frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \text{ N m}^2 \text{ C}^{-2}$ in $SI$ units). (in $\text{ cm}$)

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

The ratio of the forces between two small spheres with constant charge $(a)$ in air and $(b)$ in a medium of dielectric constant $K$ is: