An infinitely long positively charged straight thread has a linear charge density . An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of electron a

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Solution

Q.
An infinitely long positively charged straight thread has a linear charge density $λ$ $C m^{- 1}$ . An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of electron as a function of radius of circular path from the wire is [2024]

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Ans.
(2)

Electric field E at a distance r due to infinite long wire is $E = \frac{2 k λ}{r}$

Force of electron, $F = e E \Rightarrow F = e (\frac{2 k λ}{r}) = \frac{2 k λ e}{r}$

This force will provide the required centripetal force.

$F = \frac{m v^{2}}{r} = \frac{2 k λ e}{r} \Rightarrow v = \sqrt{\frac{2 k λ e}{m}}$

$K E = \frac{1}{2} m v^{2} = \frac{1}{2} m (\frac{2 k λ e}{m}) = k λ e = constant$

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