In a region, electric field varies as $E = 2x^2 -4$ where $x$ is the distance in metre from origin along $x-$ axis. A positive charge of $1\,\mu C$ is released with minimum velocity from infinity for crossing the origin, then
The kinetic energy at the origin may be zero
The kinetic energy at the origin must be zero
The kinetic energy at $x = \sqrt 2\,m$ must be zero
The kinetic energy at $x = \sqrt 2\,m$ may be zero
An electron with an initial speed of $4.0 \times 10^6 \,ms ^{-1}$ is brought to rest by an electric field. The mass and charge of an electron are $9 \times 10^{-31} \,kg$ and $1.6 \times 10^{-19} \,C$, respectively. Identify the correct statement.
In Millikan's experiment, an oil drop having charge $q$ gets stationary on applying a potential difference $V$ in between two plates separated by a distance $d$. The weight of the drop is
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
In space of horizontal $EF$ ($E = (mg)/q$) exist as shown in figure and a mass $m$ attached at the end of a light rod. If mass $m$ is released from the position shown in figure find the angular velocity of the rod when it passes through the bottom most position
A proton is accelerated through $50,000\, V$. Its energy will increase by