Two positive ions, each carrying a charge $q,$ are separated by a distance $d.$ If $F$ is the force of repulsion between the ions, the number of electrons missing from each ion will be ($e$ being the charge on an electron)
$\frac{{4\pi {\varepsilon _0}F{d^2}}}{{{e^2}}}$
$\sqrt {\;\frac{{4\pi {\varepsilon _0}F{e^2}}}{{{d^2}}}} $
$\sqrt {\;\frac{{4\pi {\varepsilon _0}F{d^2}}}{{{e^2}}}} $
$\;\frac{{4\pi {\varepsilon _0}F{d^2}}}{{{q^2}}}$
Two identical tennis balls each having mass $m$ and charge $q$ are suspended from a fixed point by threads of length $l$. What is the equilibrium separation when each thread makes a small angle $\theta$ with the vertical?
A charge $q$ is placed at the centre of the line joining two equal charges $Q$. The system of the three charges will be in equilibrium, if $q$ is equal to
A paisa coin is made up of $\mathrm{Al - Mg}$ alloy and weighs $0.75\, g$ It is electrically neutral and contains equal amounts of positive and negative charge of magnitude $34.8$ $\mathrm{kC}$. Suppose that these equal charges were concentrated in two point charges separated by :
$(i)$ $1$ $\mathrm{cm}$ $(\sim \frac{1}{2} \times $ diagonal of the one paisa coin $)$
$(ii)$ $100\,\mathrm{m}$ $(\sim $ length of a long building $)$
$(iii)$ $10^6$ $\mathrm{m}$ (radius of the earth).
Find the force on each such point charge in each of the three cases. What do you conclude from these results ?
The electrostatic force on a small sphere of charge $0.4 \;\mu\, C$ due to another small sphere of charge $-0.8 \;\mu \,C$ in air is $0.2\; N .$
$(a)$ What is the distance between the two spheres?
$(b)$ What is the force on the second sphere due to the first?
Four point $+ve$ charges of same magnitude $(Q)$ are placed at four corners of a rigid square frame as shown in figure. The plane of the frame is perpendicular to $Z$ axis. If a $-ve$ point charge is placed at a distance $z$ away from the above frame $(z<< L)$ then