A very long solenoid of circular cross section with radius a= 5.10 cm has n= 70.

Question

A very long solenoid of circular cross section with radius a= 5.10 cm has n= 70.0 turns/cm of wire. An electron is sitting outside the solenoid, at a distance r= 5.60 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? keep finding E first and getting E= 7.14E-5 and then finding F and getting F=1.14E-23N and it says this is incorrect. I've checked my math, it must be my process or formula choice thats wrong. Please help a brotha.

Explanation / Answer

The changing magnetic field will create an electric field

The induced emf is o*n*A*dI/dt = 4x10^-7*7000**0.0510^2*35 = 2.5x10^-3V

So the electric field = V/2r = 2.5x10^-5/(2*0.0560) = 7.14x10^-3N/C

So the force on the electron = E*q = 7.14x10^-3N/C*1.60x10^-19C = 1.14x10^-21N

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