Two spherical conductors each of capacity $C$ are charged to potential $V$ and $-V$ . These are then connected by mean of a fine conducting wire. The loss of energy will be

Two similar tiny balls of mass $m$, each carrying charge $q$ are hung from silk thread of  length $l$ as shown in Fig. These are separated by a distance $x$ and angle $2 \theta \sim 10$. Then for equilibrium :-

In the given circuit if point $C$ is connected to the earth and a potential of $+2000\,V$ is given to the point $A$ , the potential of $B$ is.....$V$

Condenser Ahas a capacity of $15\  \mu F$ when it is filled with a medium of dielectric constant $15$. Another condenser $B$ has a capacity $1\  \mu F$ with air between the plates. Both are charged separately by a battery of $100\,V$ . After charging, both are connected in parallel without the battery and the dielectric material being removed. The common potential now is.......$V$

Potential in the $x-y$ plane is given as $V = 5(x^2 + xy)\, volts$. The electric field at the point $(1, -2)$ will be

Four identical capacitors are connected in series with a battery of $emf$ $10\,V$. The point $X$ is earthed, then the potential of point $A$ is.....$V$