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Faraday found for Case 3 that EMF is proportional to the negative time rate of change of B. EMF is also the line integral of a force/charge. The force is EMF f q dl A) B) C) D) E) The magnetic Lorentz force. an electric force. Faraday’s position the strong nuclear force. the gravitational force. an entirely new force. Entirely worth consideration. Today we identify it as electric due to Special Relativity. A time changing B creates an electric field via Faraday’s Law: dB E dl dt B E t A) Now I have no idea how to find E. B) This law suggests a familiar way to find E in all situations. C) This law suggests a familiar way to find E in sufficiently symmetrical situations. D) I see a path to finding E, but it bears no relation to anything we have previously seen. A long solenoid of cross sectional area, A, creates a magnetic field, B0(t) that is spatially uniform inside and zero outside the solenoid. B(t) dB E dl dt B dl A) Yes, yes. I already get it. B) Ah! Now I’m pretty sure I can find E. C) Still not certain how to proceed. 0 I through A long solenoid of cross sectional area, A, creates a magnetic field, B0(t) that is spatially uniform inside and zero outside the solenoid. SO: B(t) dB E dl dt 0 I solenoid A) E 2 r B 1 C) E A t r 2 B B) E A2 r t B 1 D) E A t 2 r