A long, tightly wound air-cored solenoid of radius has turns per metre. Its current…
PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electromagnetic induction and alternating-current circuits · Electromagnetic induction and alternating-current circuits
Electricity, Magnetism and Electromagnetism, Ch Faraday's law, motional emf and Lenz's law
Problem
A long, tightly wound air-cored solenoid of radius R=3.0cm has n=1200 turns per metre. Its current is driven by an external supply and increases at the steady rate dI/dt=25As−1. Treat the solenoid as infinitely long, so that its field is uniform along the axis inside and negligible outside, and neglect the fields of the small induced currents themselves.
((a)) Find the rate of change dB/dt of the field inside the solenoid.
((b)) A flat circular coil of 40 turns and radius 1.0cm is held still inside the solenoid, coaxial with it and with its plane perpendicular to the axis. Find the magnitude of the emf induced in this coil.
((c)) Find the magnitude of the induced electric field at a point 6.0cm from the axis (outside the solenoid), and evaluate ∮E⋅dl round the circle of radius 6.0cm coaxial with the solenoid.
((d)) State what your answer to (c) tells you about whether a potential V with E=−∇V can be found for this electric field.