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A metal ball of radius $R$ is placed concentrically inside a hollow metal sphere of inner radius $2R $ and outer radius $3R$. The ball is given a charge $+2Q$ and the hollow sphere a total charge $- Q$. The electrostatic potential energy of this system is :
A finite ladder is constructed by connecting several sections of $2\,\mu F,\;4\,\mu F$ capacitor combinations as shown in the figure. It is terminated by a capacitor of capacitance $C$. What value should be chosen for $C$ such that the equivalent capacitance of the ladder between the points $A$ and $B$ becomes independent of the number of sections in between......$\mu F$
A parallel plate capacitor whose capacitance $C$ is $14\, pF$ is charged by a battery to a potential difference $V =12\, V$ between its plates. The charging battery is now disconnected and a porcelin plate with $k =7$ is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of $..........pJ$. (Assume no friction)
Two capacitors each of $1\,\mu F$ capacitance are connected in parallel and are then charged by $200\;volts$ $d.c.$ supply. The total energy of their charges (in $joules$) is