If the charge on a capacitor is increased by $2$ coulomb, the energy stored in it increases by $21\%$. The original charge on the capacitor is....$C$

$(a)$ A $900 \;p\,F$ capacitor is charged by $100 \;V$ battery [Figure $(a)$]. How much electrostatic energy is stored by the capacitor?

$(b)$ The capacitor is disconnected from the battery and connected to another $90\; p\,F$ capacitor [Figure $(b)$]. What is the electrostatic energy stored by the system?

The energy density $u$ is plotted against the distance $r$ from the centre of a spherical charge distribution on a $log$-$log$ scale. The slope of obtianed straight line is :

If $E$ is the electric field intensity of an electrostatic field, then the electrostatic energy density is proportional to

A series combination of $n_1$ capacitors, each of value $C_1$ is charged by a source of potential difference $4\, V.$ When another parallel combination of $n_2$ capacitors, each of value $C_2,$ is charged by a source of potential difference $V$, it has the same (total) energy stored in it, as the first combination has. The value of $C_2,$ in terms of $C_1$ is then

A parallel plate capacitor of capacitance $C$ is connected to a battery and is charged to a potential difference $V$. Another capacitor of capacitance $2C$ is connected to another battery and is charged to potential difference $2V$. The charging batteries are now disconnected and the capacitors are connected in parallel to each other in such a way that the positive terminal of one is connected to the negative terminal of the other. The final energy of the configuration is