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

  • A

    The kinetic energy at the origin may be zero

  • B

    The kinetic energy at the origin must be zero

  • C

    The kinetic energy at $x = \sqrt 2\,m$ must be zero

  • D

    The kinetic energy at $x = \sqrt 2\,m$ may be zero

Similar Questions

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.

  • [KVPY 2013]

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