A particle of mass $1 \,{mg}$ and charge $q$ is lying at the mid-point of two stationary particles kept at a distance $'2 \,{m}^{\prime}$ when each is carrying same charge $'q'.$ If the free charged particle is displaced from its equilibrium position through distance $'x'$ $(x\,< \,1\, {m})$. The particle executes $SHM.$ Its angular frequency of oscillation will be $….\,\times 10^{8}\, {rad} / {s}$ if ${q}^{2}=10\, {C}^{2}$

For regular pentagon system shown in figure, find force on $q_0$

Check that the ratio $ke ^{2} / G m _{ e } m _{ p }$ is dimensionless. Look up a Table of Physical Constants and determine the value of this ratio. What does the ratio signify?

Two point charges $Q$ each are placed at a distance $d$ apart. A third point charge $q$ is placed at a distance $x$ from mid-point on the perpendicular bisector. The value of $x$ at which charge $q$ will experience the maximum $Coulomb's force$ is ……………

Two identical non-conducting thin hemispherical shells each of radius $R$ are  brought in contact to make a complete sphere . If a total charge $Q$ is uniformly distributed on them, how much minimum force $F$ will  be required to hold them together