Question

A long solenoid has 110 turns/cm and carries current i. An electron moves within the solenoid in a circle of radius 2.50 cm perpendicular to the solenoid axis. The speed of the electron is 0.040 c (c = speed of light). Find the current i in the solenoid.

Answer 1

Given that the number of turns per unit length is n = N/L = 110turns /cm = 11000 turns /m

                Radius is R = 2.5 cm = 2.5*10^-2 m

                 speedof electron is v = 0.040c = 0.040*3*10⁸m/s  

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          If the electron moving in uniform magnetic field then

                                      Bev = mv² /R

                                          B = mv / R*e

                                              = (9.11*10^-31 kg)(0.040*3*10⁸ m/s ) /(2.5*10^-2 m*1.602*10^-19C)  

                                              = 2.73 *10^-3 T

         The magneticfield inside the solenoid is B = ?₀*n*I

                                                                      I= B / ?_o*n     

                                                                       = 0.0027296 T / (4?*10^-7 T.m /A * 11000 turns/m )     

                                                                       =0.1975 A