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  • An electron revolves around an infinite cylindrical wire having uniform linear charge density <img alt="2 \times 10^{-8} \mathrm{C} \mathrm{m}^{-1}" src="https://entrancecorner.oncodecogs.com/

An electron revolves around an infinite cylindrical wire having uniform linear charge density 2 \times 10^{-8} \mathrm{C} \mathrm{m}^{-1}  
in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron
with which it is revolving is ________\times 10^6 \mathrm{~m} \mathrm{~s}^{-1}.Given mass of electron =9 \times 10^{-31} \mathrm{~kg}

Option: 1

8


Option: 2

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Option: 3

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Option: 4

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Answers (1)

best_answer

In uniform circular motion

\mathrm{F}_{\mathrm{c}}=\mathrm{ma}_{\mathrm{c}}

\\ (q)(E)=\frac{m v^2}{r} \\ (e) \left(\frac{2 k \lambda}{r}\right)=\frac{m v^2}{r}

$$ \begin{aligned} & \mathrm{v}^2=\frac{(\mathrm{e})(2 \mathrm{k} \lambda)}{\mathrm{m}}=\frac{\left(1.6 \times 10^{-19}\right) \times 2 \times\left(9 \times 10^9\right) \times\left(2 \times 10^{-8}\right)}{9 \times 10^{-31}} \\ & =1.6 \times 4 \times 10^{13} \\ & \mathrm{~V}^2=16 \times 4 \times 10^{12} \Rightarrow \mathrm{v}=8 \times 10^6 \mathrm{~m} / \mathrm{s} \end{aligned}

Ans. 8

Posted by

vishal kumar

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