Two identical positive charges $Q$ each are fixed at a distance of ' $2 a$ ' apart from each other. Another point charge qo with mass ' $m$ ' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge $q_{0}$ executes $SHM$. The time period of oscillation of charge $q_{0}$ will be.
$\sqrt{\frac{4 \pi^{3} \varepsilon_{0} m a^{3}}{q_{0} Q}}$
$\sqrt{\frac{q_{0} Q}{4 \pi^{3} \varepsilon_{0} m a^{3}}}$
$\sqrt{\frac{2 \pi^{2} \varepsilon_{0} m a^{3}}{q_{0} Q}}$
$\sqrt{\frac{8 \pi^{3} \varepsilon_{0} m \alpha^{3}}{q_{0} Q}}$
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
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 : $\frac{1}{{\left( {4\pi {\varepsilon _0}} \right)}} = 9 \times {10^9}\,Nm/{C^2}$)
An isolated solid metallic sphere is given $ + Q$ charge. The charge will be distributed on the sphere
In a medium, the force of attraction between two point charges, distance $d$ apart, is $F$. What distance apart should these point charges be kept in the same medium, so that the force between them becomes $16\, F$ ?
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 ?