There is an electric field $E$ in $X$-direction. If the work done on moving a charge $0.2\,C$ through a distance of $2\,m$ along a line making an angle $60^\circ $ with the $X$-axis is $4.0\;J$, what is the value of $E$........ $N/C$

An $\alpha$ particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particals will be.

Electrostatic potential energy of given system will be

Two charges $-q$ and $+q$ are located at points $(0,0,-a)$ and $(0,0, a)$ respectively.

$(a)$ What is the electrostatic potential at the points $(0,0, z)$ and $(x, y, 0) ?$

$(b)$ Obtain the dependence of potential on the distance $r$ of a point from the origin when $r / a\,>\,>\,1$

$(c)$ How much work is done in moving a small test charge from the point $(5,0,0)$ to $(-7,0,0)$ along the $x$ -axis? Does the answer change if the path of the test charge between the same points is not along the $x$ -axis?

On rotating a point charge having a charge $q$ around a charge $Q$ in a circle of radius $r$. The work done will be

Charges $-q,\, q,\,q$ are placed at the vertices $A$, $B$, $C$ respectively of an equilateral triangle of side $'a'$ as shown in the figure. If charge $-q$ is released keeping remaining two charges fixed, then the kinetic energy of charge $(-q)$ at the instant when it passes through the mid point $M$ of side $BC$ is