A particle $A$ has charge $ + q$ and a particle $B$ has charge $ + \,4q$ with each of them having the same mass $m$. When allowed to fall from rest through the same electric potential difference, the ratio of their speed $\frac{{{v_A}}}{{{v_B}}}$ will become

A two point charges $4 q$ and $-q$ are fixed on the $x-$axis at $x=-\frac{d}{2}$ and $x=\frac{d}{2},$ respectively. If a third point charge $'q'$ is taken from the origin to $x = d$ along the semicircle as shown in the figure, the energy of the charge will

A bullet of mass $m$ and charge $q$ is fired towards a solid uniformly charged sphere of radius $R$ and total charge $+ q$. If it strikes the surface of sphere with speed $u$, find the minimum speed $u$ so that it can penetrate through the sphere. (Neglect all resistance forces or friction acting on bullet except electrostatic forces)

Four equal charges $Q$ are placed at the four corners of a square of each side is $'a'$. Work done in removing a charge $-Q$ from its centre to infinity is

Consider a system of three charges $\frac{\mathrm{q}}{3}, \frac{\mathrm{q}}{3}$ and $-\frac{2 \mathrm{q}}{3}$ placed at points $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$, respectively, as shown in the figure,

Take $\mathrm{O}$ to be the centre of the circle of radius $\mathrm{R}$ and angle $\mathrm{CAB}=60^{\circ}$

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A proton and an anti-proton come close to each other in vacuum such that the distance between them is $10 \,cm$. Consider the potential energy to be zero at infinity. The velocity at this distance will be ........... $\,m / s$