Three charges are placed along $x$-axis at $x=-a, x=0$ and $x=a$ as shown in the figure. The potential energy of the system is
$-\left(\frac{1}{4 \pi \varepsilon_0}\right) \frac{q^2}{a}$
$-\left(\frac{1}{4 \pi \varepsilon_0}\right) \frac{3 q^2}{2 a}$
$+\left(\frac{1}{4 \pi \varepsilon_0}\right) \frac{q^2}{a}$
$+\left(\frac{1}{4 \pi \varepsilon_0}\right) \frac{3 q^2}{2 a}$
A particle of charge $q$ and mass $m$ is subjected to an electric field $E = E _{0}\left(1- ax ^{2}\right)$ in the $x-$direction, where $a$ and $E _{0}$ are constants. Initially the particle was at rest at $x=0 .$ Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is
Two positive charges of magnitude $q$ are placed at the ends of a side $1$ of a square of side $2a$. Two negative charges of the same magnitude are kept at the other corners. Starting from rest, if a charge $Q$, moves from the middle of side $1$ to the centre of square, its kinetic energy at the centre of square is
In the following diagram the work done in moving a point charge from point $P$ to point $A$, $B$ and $C$ is respectively as $W_A$, $W_B$ and $W_C$ , then
A small sphere of mass $m =\ 0.5\, kg$ carrying a positive charge $q = 110\ \mu C$ is connected with a light, flexible and inextensible string of length $r = 60 \ cm$ and whirled in a vertical circle. If a vertically upwards electric field of strength $E = 10^5 NC^{-1}$ exists in the space, The minimum velocity of sphere required at highest point so that it may just complete the circle........$m/s$ $(g = 10\, ms^{-2})$
If $50$ joule of work must be done to move an electric charge of $2 \,C$ from a point, where potential is $-10$ volt to another point, where potential is $V$ volt, the value of $V$ is ......... $V$