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

An electric field due to a positively charged long straight wire at a distance $r$ from it is proportional to $r^{-1}$ in magnitude. Two electrons are orbiting such a long straight wire in circular orbits of radii $1 A$ and $2 A$. The ratio of their respective time periods is

An infinite number of charges, each of charge $1 \,\mu C$ are placed on the $x$-axis with co-ordinates $x = 1, 2,4, 8, ….\infty$. If a charge of $1\, C$ is kept at the origin, then what is the net force acting on $1\, C$ charge….$N$

Two identically charged pith balls are suspended from the some point by two massless identical threads density of each ball is $\rho $. If system is immersed in a medium of density $\sigma $, balls remain undeflected, then the dielectric constant of medium is

$5$ charges each of magnitude $10^{-5} \,C$ and mass $1 \,kg$ are placed (fixed) symmetrically about a movable central charge of magnitude $5 \times 10^{-5} \,C$ and mass $0.5 \,kg$ as shown in the figure given below. The charge at $P_1$ is removed. The acceleration of the central charge is [Given, $\left.O P_1=O P_2=O P_3=O P_4=O P_5=1 m , \frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\right]$