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
$\frac{1}{{4\pi \,{ \in _0}}}\frac{{qQ}}{{2d\left( {d + L} \right)}}$
$\frac{1}{{4\pi \,{ \in _0}}}\frac{{2qQ}}{{d\left( {d + L} \right)}}$
$\frac{1}{{4\pi \,{ \in _0}}}\frac{{qQ}}{{3d\left( {d + L} \right)}}$
$\frac{1}{{4\pi \,{ \in _0}}}\frac{{qQ}}{{d\left( {d + L} \right)}}$
A parallel plate capacitor with air between the plates has a capacitance of $9\ pF$ . The separation between its plates is $ 'd'$ .The space between the plates is now filled with two dielectrics. One of the dielectric has dielectric constant $K_1 = 6$ and thickness $\frac {d}{3}$ while the other one has dielectric constant $K_2 = 12$ and thickness $\frac {2d}{3}$ . Capacitance of the capacitor is now ......... $pF$
Five point charges each having magnitude $'q'$ are placed at the corners of regular hexagon as shown in figure. Net electric field at the centre $'O'$ is $\vec E$ . To get net electric field at $'O'$ to be $6\vec E$ , charge placed on the remaining sixth corner should be
The electric field $\vec E$ between two points is constant in both magnitude and direction. Consider a path of length d at an angle $\theta = 60^o$ with respect to field lines shown in figure. The potential difference between points $1$ and $2$ is
Capacity of an isolated sphere is increased $n$ times when it is enclosed by an earthed concentric sphere. The ratio of their radii is
Electric field inside a uniformly charged sphere of radius $R,$ is ($r$ is distance from centre, $r < R$)