A very long solenoid of circular cross section with radius r=3.20cm has n= 79.0

Question

A very long solenoid of circular cross section with radius r=3.20cm has n= 79.0 turns/cm of wire. An electron is sitting outsidethe solenoid, at a distance r= 3.70 cm from the solenoid axis. Whatis the magnitude of the force on the electron while the current inthe solenoid is ramped up at a rate of 35.0 Amps/second? Hint: Use Faraday's Law to calculate the lineintegral of the electric field around a circular path of radius r.Then use F=qE. A very long solenoid of circular cross section with radius r=3.20cm has n= 79.0 turns/cm of wire. An electron is sitting outsidethe solenoid, at a distance r= 3.70 cm from the solenoid axis. Whatis the magnitude of the force on the electron while the current inthe solenoid is ramped up at a rate of 35.0 Amps/second? Hint: Use Faraday's Law to calculate the lineintegral of the electric field around a circular path of radius r.Then use F=qE.

Explanation / Answer

B field in solenoid = u n i . induced emf = - d (BA) / dt  =    A dB/dt   = r2 u n di/dt . induced emf also = integral of (E ds ) =   E 2 R .     So...    r2u n di/dt = E 2R      or .       E = r2 un di/dt / 2 R . Force = chare * E = q r2 un di/dt / 2 R = .      = 1.60 x 10-19 *0.03202 * 4 x 10-7 * 7900 * 35.0 /2 * 0.0370 = .         = 0.7695 x 10-21 Newtons

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