Six charges $+ q ,- q ,+ q ,- q ,+ q$ and $- q$ are fixed at the corners of a hexagon of side $d$ as shown in the figure. The work done in bringing a charge $q _0$ to the centre of the hexagon from infinity is :$\left(\varepsilon_0-\right.$ permittivity of free space)

A ball of mass $1\, g$ and charge ${10^{ - 8}}\,C$ moves from a point $A$. where potential is $600\, volt$ to the point $B$ where potential is zero. Velocity of the ball at the point $B$ is $20\, cm/s$. The velocity of the ball at the point $A$ will be

A point chargr $Q$ is fixed A small charge $q$ and mass $m$ is given a velocity $v_0$ from infinity & perpendicular distance $r_0$ as shown. If distance of closest approach is $r_0/2$. The value of $q$ is [Given $mv_0^2 = \frac{{{Q^2}}}{{4\pi { \in _0}\,{r_0}}}$]

In the figure shown the electric potential energy of the system is: ( $q$ is at the centre of the conducting neutral spherical shell of inner radius $a$ and outer radius $b$ )

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.

Electric field at a place is $\overrightarrow {E\,}  = {E_0}\hat i\,V/m$ . A particle of charge $+q_0$  moves from point $A$ to $B$ along a circular path find work done in this motion by electric field