An infinite non-conducting sheet has a surface charge density $\sigma = 0.10 \, \mu C/m^2$ on one side. How far apart are equipotential surfaces whose potentials differ by $50 \, V$?

An infinitely long positively charged straight thread has a linear charge density $\lambda \text{ Cm}^{-1}$. An electron revolves along a circular path having its axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of the electron as a function of the radius $r$ of the circular path from the wire is:

Consider a thin spherical shell of radius $R$ with its centre at the origin,carrying uniform positive surface charge density. The variation of the magnitude of the electric field $|\vec{E}(r)|$ and the electric potential $V(r)$ with the distance $r$ from the centre,is best represented by which graph?

Obtain Coulomb's law from Gauss's law.

$A$ long cylindrical volume contains a uniformly distributed charge of density $\rho$. The radius of the cylindrical volume is $R$. $A$ charged particle $(q)$ revolves around the cylinder in a circular path at a distance $r$ from the axis. The kinetic energy of the particle is:

Two parallel infinite line charges with linear charge densities $+\lambda\; C/m$ and $-\lambda\; C/m$ are placed at a distance of $2R$ in free space. What is the electric field mid-way between the two line charges?