Four charges equal to $-Q$ are placed at the four corners of a square and a charge $q$ is at its centre. If the system is in equilibrium the value of $q$ is
$ - \frac{Q}{4}(1 + 2\sqrt 2 )$
$\frac{Q}{4}(1 + 2\sqrt 2 )$
$ - \frac{Q}{2}(1 + 2\sqrt 2 )$
$\frac{Q}{2}(1 + 2\sqrt 2 )$
Two charges each of magnitude $Q$ are fixed at $2a$ distance apart. A third charge ($-q$ of mass $'m'$) is placed at the mid point of the two charges; now $-q$ charge is slightly displaced perpendicular to the line joining the charges then find its time period
Two identical charged spheres suspended from a common point by two massless strings of lengths $l,$ are initially at a distance $d\;(d < < l)$ apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity $v.$ Then $v$ varies as a function of the distance $x$ between the spheres, as
Two positively charged spheres of masses $m_1$ and $m_2$ are suspended from a common point at the ceiling by identical insulating massless strings of length $l$. Charges on the two spheres are $q_1$ and $q_2$, respectively. At equilibrium, both strings make the same angle $\theta$ with the vertical. Then
The value of electric permittivity of free space is
A given charge is situated at a certain distance from an electric dipole in the end-on position experiences a force $F$. If the distance of the charge is doubled, the force acting on the charge will be