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 $2\,\mu F$ capacitor is charged to a potential $=10\ V$ . Another $4\,\mu F$ capacitor is charged to a potential $= 20\ V$ . The two capacitors are then connected in a single loop, with the positive plate of one connected with negative plate of the other. What heat is evolved in the circuit ?.........$\mu J$

Two charges  $ + 3.2\, \times \,{10^{ - 19}}\,C$ and $ - 3.2\, \times \,{10^{ - 19}}\,C$ kept $2.4\,\mathop A\limits^o $ apart forms a dipole. If it is kept in uniform electric field of intensity $4\, \times \,{10^{5\,}}\,volt/m$ then what will be its potential energy in stable equilibrium

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

Three identical uncharged metal spheres are at the vertices of an equilateral triangle. One at a time, a small sphere is connected by a conducting wire with a large metal sphere that is charged. The center of the large sphere is in the straight line perpendicular to the plane of equilateral triangle and passing through its centre (see figure). As a result, the first small sphere acquires charge $q_1$ and second charge $q_2 (q_2 < q_1)$ . The charge that the third sphere $q_3$ will acquire is (Assume $l >> R$ , $l >> r$ , $d >> R$ , $d >> r$ )

If the charge on a capacitor is increased by $2\, C$ the energy stored in it increases by $21\%$. The original charge on the capacitor (in coulomb) is