If an $\alpha$-particle and a proton are accelerated from rest by a potential difference of 1 megavolt then the ratio of their kinetic energy will be

A unit positive point charge of mass $m$ is projected with a velocity $V$ inside the tunnel as shown. The tunnel has been made inside a uniformly charged non conducting sphere. The minimum velocity with which the point charge should be projected such it can it reach the opposite end of the tunnel, is equal to

Two identical particles of mass $m$ and charge $q$ are shot at each other from a very great distance with an initial speed $v$. The distance of closest approach of these charges is

When a charge of $3\, coulomb$ is placed in a uniform electric field, it experiences a force of $3000\, Newton$. Within this field, potential difference between two points separated by a distance of $1\, cm$ is........$volts$

Charge $q_{2}$ is at the centre of a circular path with radius $r$. Work done in carrying charge $q_{1}$, once around this equipotential path, would be

In a region of space, suppose there exists a uniform electric field $\vec{E}=10 i\left(\frac{ v }{ m }\right)$. If a positive charge moves with a velocity $\vec{v}=-2 \hat{j}$, its potential energy