Three point charges $+q, -2q$ and $+q$ are placed at points $(x = 0, y = a, z = 0), (x = 0, y = 0,z = 0)$ and $(x = a, y = 0, z = 0)$ respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are
$\sqrt 2\,qa$ along $+ y$ direction
$\sqrt 2\,qa$ along the line joining points $(x = 0, y = 0, z = 0)$ and $(x = a, y = a, z = 0)$
$qa$ along the line joining points $(x = 0, y = 0, z = 0)$ and $(x = a, y = a, z = 0)$
$\sqrt 2\,qa$ along $+ x$ direction
Two identical charged spheres suspended from a common point by two massless strings of length $l$ are initially a distance $d(d << I) $ apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result charges approach each other with a velocity $v$. Then as a function of distance $x$ between them,
Four metallic plates, each with a surface area of one side $A$, are placed at a distance $d$ from each other. The plates are connected as shown in the figure. The capacitance of the system between $a$ and $b$ is
Four dipoles having charge $ \pm e$ are placed inside a sphere. The total flux of ${\vec E}$ coming out of the sphere is
Two capacitors $C_1$ and $C_2$ are are charged to $120\, V$ and $200\, V$ respectively. It is found that by connecting them together the potential on each one can be made zero . Then
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 ?.........$\mu J$