The electrostatic force of interaction between an uniformly charged rod having total charge $Q$ and length $L$ and a point charge $q$ as shown in figure is
$\frac{1}{{4\pi { \in _0}}}\frac{{qQ}}{{d(d + L)}}$
$\frac{1}{{4\pi { \in _0}}}\frac{4{qQ}}{{(2d + L)^2}}$
$\frac{1}{{4\pi { \in _0}}}\frac{{Qq}}{{d^2}}$
$\frac{1}{{4\pi { \in _0}}}\frac{{qQ}}{{{{(d + L)}^2}}}$
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
Two copper balls, each weighing $10\,g$ are kept in air $10\, cm$ apart. If one electron from every ${10^6}$ atoms is transferred from one ball to the other, the coulomb force between them is (atomic weight of copper is $63.5$)
Two identical conducting spheres carrying different charges attract each other with a force $F$ when placed in air medium at a distance $'d'$ apart. The spheres are brought into contact and then taken to their original positions. Now the two spheres repel each other with a force whose magnitude is equal to that of the the initial attractive force. The ratio between initial charges on the spheres is
Two identical charged particles each having a mass $10 \,g$ and charge $2.0 \times 10^{-7}\,C$ area placed on a horizontal table with a separation of $L$ between then such that they stay in limited equilibrium. If the coefficient of friction between each particle and the table is $0.25$, find the value of $L$.[Use $g =10\,ms ^{-2}$ ]..........$cm$
Two charges $-\mathrm{q}$ each are fixed separated by distance $2\mathrm{d}$. A third charge $\mathrm{d}$ of mass $m$ placed at the midpoint is displaced slightly by $x (x \,<\,<\, d)$ perpendicular to the line joining the two fixed charged as shown in figure. Show that $\mathrm{q}$ will perform simple harmonic oscillation of time period. $T =\left[\frac{8 \pi^{3} \epsilon_{0} m d^{3}}{q^{2}}\right]^{1 / 2}$