Consider a solid insulating sphere of radius $R$ with charge density varying as $\rho = \rho _0r^2$ ($\rho _0$ is a constant and $r$ is measure from centre). Consider two points $A$ and $B$ at distance $x$ and $y$ respectively $(x < R, y > R)$ from the centre. If magnitudes of electric fields at points $A$ and $B$ are equal, then
${x^2}y = {R^3}$
${x^3}y^2 = {R^5}$
${x^2}y^3 = {R^5}$
$\frac{{{x^4}}}{y} = {R^5}$
Two spherical conductors each of capacity $C$ are charged to potential $V$ and $-V$ . These are then connected by mean of a fine conducting wire. The loss of energy will be
What is the angle between the electric dipole moment and the electric field strength due to it on the equatorial line.......$^o$
The plates of a parallel plate capacitor are charged up to $100\,volt$. A $2\,mm$ thick plate is inserted between the plates, then to maintain the same potential difference, the distance between the capacitor plates is increased by $1.6\,mm$. The dielectric constant of the plate is
If the charge on a capacitor is increased by $2\, C$ the energy stored in it increases by $21\%$. The original charge on the capacitor (in coulomb) is
A point charge $q$ is situated at a distance $d$ from one end of a thin non - conducting rod of length $L$ having a charge $Q$ (uniformly distributed along its length) as shown in fig.Then the magnitude of electric force between them is