An electron revolves around an infinite cylindrical wire having...

The electric field is given by

$E = \left(\dfrac{2k\lambda}{r}\right)$

The required centripetal force is

$F = \left(\dfrac{m{v}^{2}}{r}\right)$

The force due to the field is equal to the required centripetal force,

$⇒ \left(\dfrac{2k\lambda}{r}\right)e = \dfrac{m{v}^{2}}{r}$

$⇒ v = \sqrt{\dfrac{2k\lambdae}{m}} = \sqrt{\dfrac{2 \times 9 \times {10}^{9} \times 2 \times {10}^{- 8} \times 1 . 6 \times {10}^{- 19}}{9 \times {10}^{- 31}}}$

$= \sqrt{1 . 6 \times 4 \times {10}^{13}} = 4 \times 2 \times {10}^{6}m{s}^{- 1}$

$= 8 \times {10}^{6}m{s}^{- 1}$