Question

A very long solenoid of circular cross section with radius a= 2.60 cm has n= 71.0 turns/cm of wire. An electron is sitting outside the solenoid, at a distance r= 3.10 cm from the solenoid axis. What is the magnitude of the force on the electron while the current in the solenoid is ramped up at a rate of 36.0 Amps/s?

answer is not 5.6x10^-14 or 5.6x10^-22

Answer 1

given

long solenoid with circular cross section with radius a= 2.60 cm has n= 71.0 turns/cm of wire

a = 2.60 cm, n = 71.0 turns/cm

electron is at r = 3.10 cm from the axis out side the solenoid

di/dt = 36 amperes/s

here

the current is changing so that it creates the induced emf

the induced emf is e = mue0*n*A di/dt

e = 4pi*10^-7*7100*pi*(2.60*10^-2)^2*36 V

e = 0.0006821302073 V

from the relation between the electric field and potential is

V = E*d

E =V/d

= e/2pi*a

= 0.0006821302073/(2pi*2.60*10^-2) N/C

= 0.0041755536278 N/C

so the force on electron is  

F = E*q

F = 0.0041755536278*1.6*10^-19

F = 6.681*10^-22 N