Question

A very long solenoid of circular cross section with radius a= 4.40 cm has n= 65.0 turns/cm of wire. An electron is sitting outside the solenoid, at a distance r= 4.90 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 35.0 Amps/s?

Answer 1

the changing current will cause changing magnetic field and changing magnetic field in will create an electric field

induced emf = μo * n * A * dI/dt

area A = pi * radius^2

induced emf = 4 * π * 10^-7 * 6500 * π * 0.044^2 * 35

induced emf = 0.001738 V

electric field = induced emf / 2πr

electric field = 0.001738 / (2 * π * 0.044)

force on the electron = electric field * charge

force = (0.001738 / (2 * π * 0.044)) * 1.60 * 10^-19

force = 1.0058592 * 10^-21 N