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

Electric potential at an equatorial point of a small dipole with dipole moment $P$  ( $r$ , distance from the dipole) 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.......$\mu F$

Three charges $2q,\, - q,\, - q$ are located at the vertices of an equilateral triangle. At the centre of the triangle

What is the equivalent capacitance of the system of capacitors between $A$ and $B$ :-

The plates of a parallel plate capacitor are charged up to $100\, volt$ . A $2\, mm$ thick plate is inserted between the plates, then to maintain the same potential difference, the distance between the capacitor plates is increased by $1.6\, mm$ . The dielectric constant of the plate is