A long solenoid has 70   turns   cm - 1 and carries current I . An electron moves within the solenoid in a circle of radius 2 . 5   cm perpendicular to the solenoid axis. If the speed of the electron is 4 . 4 × 10 6   m   s - 1 then the current I in the solenoid is (Take μ 0 = 4 π × 10 - 7 SI unit, mass of electron = 9 × 10 - 31   kg , charge of electron = 1 . 6

Step-by-step solution

Given: n = 70   turns   cm - 1 = 7000   turns   m - 1 and r = 2 . 5   cm = 0 . 025   m Now centripetal force will be provided by the magnetic force acting on the charge. Therefore, m v 2 r = q B v and we also know that for long solenoid, B = μ 0 n I . So, m v 2 r = q μ 0 n I v ⇒ I = m v 2 μ 0 n r = 9 × 10 - 31 4 . 4 × 10 6 2 4 π × 10 - 7 7000 0 . 025 = 112 . 5   mA