An infinite number of identical capacitors each of capacitance $1 \mu F$ are connected as shown in the figure. Then, the equivalent capacitance between $A$ and $B$ is .......... $\mu F$

Two point charges $+8q$ and $-2q$ are located at $x = 0$ and $x = L$ respectively. The location of a point on the $x-$ axis at which the net electric field due to these two point charges is zero is

A hollow cylinder has a charge $q$ coulomb within it. If $\phi $ is the electric flux in units of voltmete associated with the curved surface $B$ , the flux linked with the plane surface $A$ in units of volt-meter will be

A solid coducting sphere having a charge $Q$ is surrounded by an uncharged concentric  conducting hollow spherical shell. Let the potential difference between the surface of the  solid sphere and that of the outer surface of the hollow shell be $V$. If the shell is now  given a charge $-3Q$, the new potential difference between the same two surface 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

If the distance between the plates of a capacitor having capacity $C$ and charge $Q$ is doubled then work done will be