Question

An infinitely long positively charged straight thread has a linear charge density λ Cm^–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 :

(1)

(2)

(3)

(4)

Answer 1

Correct option is : (2)

Electric field E at a distance r due to infinite long wire is \(\frac{2kλ}{r}\)

Force of electron \(\Rightarrow \mathrm{F}=\mathrm{eE}\)

\(\mathrm{F}=\mathrm{e}\left(\frac{2 \mathrm{k} \lambda}{\mathrm{r}}\right)\)

\(\mathrm{F}=\frac{2 \mathrm{k} \lambda \mathrm{e}}{\mathrm{r}}\)

This force will provide required centripetal force

\(\mathrm{F}=\frac{\mathrm{mv}^{2}}{\mathrm{r}}=\frac{2 \mathrm{k} \lambda \mathrm{e}}{\mathrm{r}}\)

\(v=\sqrt{\frac{2 \mathrm{k} \lambda \mathrm{e}}{\mathrm{m}}}\)

\(\mathrm{KE} =\frac{1}{2} \mathrm{mv}^{2}=\frac{1}{2} \mathrm{~m}\left(\frac{2 \mathrm{k} \lambda \mathrm{e}}{\mathrm{m}}\right) \)

\(=\mathrm{k} \lambda \mathrm{e}\)