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Consider the arrangement shown in figure. The total energy stored is $U_1$ when key is closed. Now the key $K$ is made off (opened) and two dielectric slabs of relative permittivity ${ \in _r}$ are introduced between the plates of the two capacitors. The slab tightly fit in between the plates. The total energy stored is now $U_2$. Then the ratio of $U_1/U_2$ is
A thin-walled, spherical conducting shell $S$ of radius $R$ is given charge $Q$. The same amount of charge is also placed at its centre $C. $ Which of the following statements are correct ?
Charge $q_{2}$ is at the centre of a circular path with radius $r$. Work done in carrying charge $q_{1}$, once around this equipotential path, would be
$n$ the rectangle, shown below, the two corners have charges ${q_1} = - 5\,\mu C$ and ${q_2} = + 2.0\,\mu C$. The work done in moving a charge $ + 3.0\,\mu C$ from $B$ to $A$ is.........$J$ $(1/4\pi {\varepsilon _0} = {10^{10}}\,N{\rm{ - }}{m^2}/{C^2})$
Three plates $A, B$ and $C$ each of area $0.1 \ m^2$ are separated by $0.885\ mm$ from each other as shown in the figure. $A$ $10$ $V$ battery is used to charge the system. The energy stored in the system is
The electric field between the plates of a parallel plate capacitor when connected to a certain battery is ${E_0}$. If the space between the plates of the capacitor is filled by introducing a material of dielectric constant $K$ without disturbing the battery connections, the field between the plates shall be