Two concentric spheres $A$ and $B$ are kept very near to each other. $A$ is negatively charged and $B$ is earthed. The true statement is

$(A)$ Charge on $B$ is zero
$(B)$ Potential at $B$ is zero
$(C)$ Charge is uniformly distributed on $A$
$(D)$ Charge is non uniformly distributed on $A$

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.......$\mu F$

A wheel having mass $m$ has charges $+q$ and $-q$ on diametrically opposite points. It  remains in equilibrium on a rough inclined plane in the presence of uniform horizontal  electric field $E =$

The electric potential $V$ at any point $O$ ($x, y, z$ all in metre) in space is given by $V=4x^2\, volt$. The electric field at the point $(1\,m, 0, 2\,m)$ in $volt/meter$ is

A parallel plate condenser has a uniform electric field $E(V/m)$ in the space between the plates. If the distance between the plates is $d(m)$ and area of each plate is $A(m^2)$, then the energy (joules) stored in the condenser is

The equivalent capacitance of the system of capacitors between $A$ and $B$ as shown in the figure