Two charges ${q_1}$ and ${q_2}$ are placed in vacuum at a distance $d$ and the force acting between them is $F$. If a medium of dielectric constant $4$ is introduced around them, the force now will be
$4F$
$2F$
$\frac{F}{2}$
$\frac{F}{4}$
Two identical conducting spheres carry identical charges. If the spheres are set at a certain distance apart, they repel each other with a force $F$. A third conducting sphere identical to the other two, but initially uncharged is touched to one sphere and then to the other before being removed. The force between the original two spheres is now
A certain charge $Q$ is divided into two parts $q$ and $(Q-q) .$ How should the charges $Q$ and $q$ be divided so that $q$ and $(Q-q)$ placed at a certain distance apart experience maximum electrostatic repulsion?
Figure represents a crystal unit of cesium chloride, $\mathrm{CsCl}$. The cesium atoms, represented by open circles are situated at the corners of a cube of side $0.40\,\mathrm{nm}$, whereas a $\mathrm{Cl}$ atom is situated at the centre of the cube. The $\mathrm{Cs}$ atoms are deficient in one electron while the $\mathrm{Cl}$ atom carries an excess electron.
$(i)$ What is the net electric field on the $\mathrm{Cl}$ atom due to eight $\mathrm{Cs}$ atoms ?
$(ii)$ Suppose that the $\mathrm{Cs}$ atom at the corner $A$ is missing. What is the net force now on the $\mathrm{Cl}$ atom due to seven remaining $\mathrm{Cs}$ atoms ?
Two small spherical balls each carrying a charge $Q = 10\,\mu C$ ($10\, micro-coulomb$) are suspended by two insulating threads of equal lengths $3\, m$ each, from a point fixed in the ceiling. It is found that in equilibrium threads are separated by an angle $120^o$ between them, as shown in the figure. What is the tension in the threads (Given : $\frac{1}{{\left( {4\pi {\varepsilon _0}} \right)}} = 9 \times {10^9}\,Nm/{C^2}$)
Two small spheres each having the charge $ + Q$ are suspended by insulating threads of length $L$ from a hook. This arrangement is taken in space where there is no gravitational effect, then the angle between the two suspensions and the tension in each will be