At a point $20\, cm$ from the centre of a uniformly charged dielectric sphere of radius $10\, cm$, the electric field is $100\, V/m$. The electric field at $3\, cm$ from the centre of the sphere will be.......$V/m$.

An electric field converges at the origin whose magnitude is given by the expression $E = 100\,r\,N/C$,where $r$ is the distance measured from the origin.

Find the electric field due to an infinitely long charged cylinder of radius $R$ having a linear charge density $\lambda$ at a distance of $R/2$ from its axis.

An infinitely long thin straight wire has a uniform linear charge density of $\frac{1}{3} \, C \cdot m^{-1}$. The magnitude of the electric field intensity at a point $18 \, cm$ away is (given $\varepsilon_0 = 8.85 \times 10^{-12} \, C^2 \cdot N^{-1} \cdot m^{-2}$):

Within a spherical charge distribution of charge density $\rho(r)$,$N$ equipotential surfaces of potential $V_0, V_0 + \Delta V, V_0 + 2\Delta V, \dots, V_0 + N\Delta V$ (where $\Delta V > 0$) are drawn and have increasing radii $r_0, r_1, r_2, \dots, r_N$,respectively. If the difference in the radii of the surfaces is constant for all values of $V_0$ and $\Delta V$,then:

Let a total charge $2Q$ be distributed in a sphere of radius $R$,with the charge density given by $\rho(r) = kr$,where $r$ is the distance from the centre. Two charges $A$ and $B$,of $-Q$ each,are placed on diametrically opposite points,at equal distance $a$ from the centre. If $A$ and $B$ do not experience any force,then: