Question

A long solenoid has 110 turns/cm and carries current i. An electron moves within the solenoid in a circle of radius 2.54 cm perpendicular to the solenoid axis. The speed of the electron is 0.0635c (c = speed of light, equal to 2.998 × 108 m/s). 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 = 2.54 cm

                    = 2.54*10^-2 m

Speedof electron is v = 0.0635c

                                   = 0.0635*(2.998*10^8m/s)

                                   = 0.1903*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)(0.1903*10^8 m/s ) /(2.54*10^-2 m)(1.602*10^-19C)  

                                              = 0.426 *10^-2 T

    The magneticfield inside the solenoid is B = μ₀*n*I

                                                                    I= B / μ_o*n     

                                                               

= 0.426 *10^-2 T / (4π*10^-7 T.m /A * 11000 turns/m )

                                                                    =3.08 A

I hope help you.