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Two capacitors ${C_1} = 2\,\mu \,F$ and ${C_2}\, = \,6\,\mu \,F$ in series, are connected in parallel to a third capacitor ${C_3} = \,4\,\mu \,F$. This arrangement is then connected to a battery of $e.m.f.$ $=$ $2V$, as shown in the figure. How much energy is lost by the battery in charging the capacitors
$n$ 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.........$J$ $(1/4\pi {\varepsilon _0} = {10^{10}}\,N{\rm{ - }}{m^2}/{C^2})$
An electric dipole with dipole moment $\vec p = (3i + 4j) \times 10^{-30} C-m$ is placed in an electric field $\vec E = 4000 \hat i (N/C).$ An external agent turns the dipole slowly until its electric dipole moment becomes $(-4 \hat i + 3 \hat j) ×10^{-30}C-m.$ The work done by the external agent is equal to :-
Six metallic plates each with a surface area of one side $A$, are placed at a distance $d$ from each other. The alternate plates are connected to points $P$ and $Q$ as shown in figure. The capacitance of the system is
A parallel plate capacitor has a uniform electric field $E$ in the space between the plates. If the distance between the plates is $d$ and area of each plate is $A,$ the energy stored in the capacitor is
Two metal spheres $A$ and $B$ of radii $a$ and $b(a < b)$ respectively are at a large distance apart. Each sphere carries a charge of $100 \mu C$. The spheres are connected by a conducting wire, then