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
$\frac{1}{2}$
$1$
$2$
$4$
An elementary particle of mass $m$ and charge $ + e$ is projected with velocity $v$ at a much more massive particle of charge $Ze,$ where $Z > 0.$What is the closest possible approach of the incident particle
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........$m/s$ $(g = 10\, ms^{-2})$
Charge $Q$ is given a displacement $\vec r = a\hat i + b\hat j$ in an electric field $\vec E = E_1\hat i + E_2\hat j$ . The work done is
A test charge $q$ is made to move in the electric field of a point charge $Q$ along two different closed paths as per figure. First path has sections along and perpendicular to lines of electric field. Second path is a rectangular loop of the same area as the first loop. How does the work done compare in the two cases ?
The diagram shows three infinitely long uniform line charges placed on the $X, Y $ and $Z$ axis. The work done in moving a unit positive charge from $(1, 1, 1) $ to $(0, 1, 1) $ is equal to