An electron revolves around an infinite cylindrical wire having uniform linear charge density in a circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of the electron with which it is revolving is ____

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Solution

Q.
An electron revolves around an infinite cylindrical wire having uniform linear charge density $2 \times 10^{- 8} {Cm}^{- 1}$ in a circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of the electron with which it is revolving is __________ $\times 10^{6} {ms}^{- 1}$ . Given, mass of electron $= 9 \times 10^{- 31} kg$ . [2023]

Ans.
(8)

$e E = \frac{m v^{2}}{r}$

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

$v = \sqrt{\frac{e \cdot 2 k λ}{m}} = \sqrt{\frac{1.6 \times 10^{- 19} \times 2 \times 9 \times 10^{9} \times 2 \times 10^{- 8}}{9 \times 10^{- 31}}}$

$= 8 \times 10^{6} m/s$

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