An electron revolves around an infinite cylindrical wire having uniform linear charge density 2 × 10 - 8 C   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 ______________ × 10 6   m   s - 1 . Given mass of electron = 9 × 10 - 31   kg

Step-by-step solution

The electric field is given by E = 2 k λ r The required centripetal force is F = m v 2 r The force due to the field is equal to the required centripetal force, ⇒ 2 k λ r e = m v 2 r ⇒ v = 2 k λ e m = 2 × 9 × 10 9 × 2 × 10 - 8 × 1 . 6 × 10 - 19 9 × 10 - 31 = 1 . 6 × 4 × 10 13 = 4 × 2 × 10 6   m   s - 1 =   8   ×   10 6   m   s - 1