Two charges are at a distance $‘d’$ apart. If a copper plate (conducting medium) of thickness $\frac{d}{2}$ is placed between them, the effective force will be

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^o$ with each other. When suspended in a liquid of density $1\, g\, cm^{-3}$, the angle remains the same. If density of the material of the sphere is $4/3\, g\, cm^{-3}$, the dielectric constant of the liquid is

Write limitation of Coulomb’s law.

The unit of electric permittivity is

Three point charges $q,-2 q$ and $2 q$ are placed on $x$-axis at a distance $x=0, x=\frac{3}{4} R$ and $x=R$ respectively from origin as shown. If $q =2 \times 10^{-6}\,C$ and $R =2\,cm$, the magnitude of net force experienced by the charge $-2 q$ is .......... $N$

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.  $T =\left[\frac{8 \pi^{3} \epsilon_{0} m d^{3}}{q^{2}}\right]^{1 / 2}$