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  4. In a uniform electric field, a point charge of mass m and charge q is released from rest. If there are no other forces acting on the particle, then which of the following graphs, correctly show the dependence of the particles speed v on the distance x travelled by it? [Graphs are schematic and not drawn to scale]

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Q. In a uniform electric field, a point charge of mass $m$ and charge $q$ is released from rest. If there are no other forces acting on the particle, then which of the following graphs, correctly show the dependence of the particles speed $v$ on the distance $x$ travelled by it? [Graphs are schematic and not drawn to scale]

NTA AbhyasNTA Abhyas 2020Electrostatic Potential and Capacitance

Solution:

Using work-energy theorem,
$qEx=\frac{1}{2}mv^{2}$
$\Rightarrow v^{2}=\frac{2 q E}{m}x\Rightarrow v=\sqrt{\frac{2 q E}{m}}\sqrt{x}$