The electric potential $(V)$ as a function of distance $(x)$ [in meters] is given by $V = (5x^2 + 10 x -9)\, Volt$. The value of electric field at $x = 1\, m$ would be......$Volt/m$

A network of four capacitors of capacity equal to $C_1 = C,$ $C_2 = 2C,$ $C_3 = 3C$ and $C_4 = 4C$ are conducted to a battery as shown in the figure. The ratio of the charges on $C_2$ and $C_4$ is

A spherical shell with an inner radius $'a'$ and an outer radius $'b'$ is made of conducting material. A point charge $+Q$ is placed at the centre of the spherical shell and a total charge $-q$ is placed on the shell. Final charge distribution on the surfaces as

Three charges $4q,\,Q$ and $q$ are in a straight line in the position of $0$, $l/2$ and $l$ respectively. The resultant force on $q$ will be zero, if $Q = $

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 vertical electric field $E =$  

Two condensers $C_1$ and $C_2$ in a circuit are joined as shown in figure. The potential of point $A$ is $V_1$ and that of $B$ is $V_2$. The potential of point $D$ will be