A charged particle $'q'$ is shot from a large distance with speed $v$ towards a fixed  charged particle $Q$. It apporaches $Q$ upto a closet distance $r$ and then returns. If $q$ were given a speed $'2v$', the closest distance of approach would be 

The work done required to put the four charges together at the corners of a square of side $a$ , as shown in the figure is

Three equal charges are placed at the corners of an equilateral triangle. Which of the graphs below correctly depicts the equally-spaced equipotential surfaces in the plane of the triangle? (All graphs have the same scale.)

An electric point charge $10^{-3}\,\mu C$ is placed at the origin $(0, 0)$ of $X-Y$ co- ordinate system. Two points $A$ and $B$ are situated at $(\sqrt 2, \sqrt 2)$ and $(2, 0)$ respectively. The potential difference between the points $A$ and $B$ will be.....$volt$

Condenser Ahas a capacity of $15\  \mu F$ when it is filled with a medium of dielectric constant $15$. Another condenser $B$ has a capacity $1\  \mu F$ with air between the plates. Both are charged separately by a battery of $100\,V$ . After charging, both are connected in parallel without the battery and the dielectric material being removed. The common potential now is.......$V$

Two charges $q_1$ and $q_2$ are placed $30\,cm$ apart, as shown in the figure. A third charge $q_3$ is moved along the arc of a circle of radius $40\,cm$ from $C$ to $D$. The change in the potential energy of the $\frac{{{q_3}}}{{4\pi \,{ \in _0}}}k$ , where $k$ is