$(a)$ Explain the meaning of the statement ‘electric charge of a body is quantised’.
$(b)$ Why can one ignore quantisation of electric charge when dealing with macroscopic i.e., large scale charges?
$(a)$ Electric charge of a body is quantized. This means that only integral $(1,2 \ldots n)$ number of electrons can be transferred from one body to the other. Charges are not transferred in fraction. Hence, a body possesses total charge only in integral multiples of electric charge.
$(b)$ In macroscopic or large scale charges, the charges used are huge as compared to the magnitude of electric charge. Hence, quantization of electric charge is of no use on macroscopic scale. Therefore, it is ignored and it is considered that electric charge is continuous.
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. $T =\left[\frac{8 \pi^{3} \epsilon_{0} m d^{3}}{q^{2}}\right]^{1 / 2}$
Four identical pendulums are made by attaching a small ball of mass $100 \,g$ on a $20 \,cm$ long thread and suspended from the same point. Now, each ball is given charge $Q$, so that balls move away from each other with each thread making an angle of $45^{\circ}$ from the vertical. The value of $Q$ is close to ..............$\mu C$ $\left(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\right.$ in $SI$ units $)$
A charge $+q$ is situated at a distance $d$ away from both the sides of a grounded conducting $L$ shaped sheet as shown in the figure.The force acting on the charge $+q$ is
The charges on two sphere are $+7\,\mu C$ and $-5\,\mu C$ respectively. They experience a force $F$. If each of them is given and additional charge of $-2\,\mu C$, the new force of attraction will be
Dielectric constant of pure water is $81$. Its permittivity will be