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

Two identical charged spheres suspended from a common point by two massless strings of length $l$ are initially a distance $d(d  << I) $ apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result charges approach each other with a velocity $v$. Then as a function of distance $x$ between them,

A parallel plate capacitor has plates with area $A$ and separation $d$. A battery charges the plates to a potential difference $V_0$. The battery is then disconnected and a dielectric slab of thickness $d$ is introduced. The ratio of energy stored in the capacitor before and after slab is introduced, is

Electric field inside a uniformly charged sphere of radius $R,$ is ($r$ is distance from centre, $r < R$)

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.....$V$

A series combination of $n_1$ capacitors, each of value $C_1$, is charged by a source of potential difference $4V$. 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