A long solenoid of radius carries a current that is being changed so that its uniform…
PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electric current and circuits · Electromagnetic induction and alternating-current circuits
Electricity, Magnetism and Electromagnetism, Ch Faraday's law, motional emf and Lenz's law
Problem
A long solenoid of radius R=3.0cm carries a current that is being changed so that its uniform interior field, directed along the axis, grows at the steady rate dB/dt=0.80Ts−1. The field outside the solenoid is negligible. Look along the axis so that B points out of the page. A circular ring of wire of radius 6.0cm, coaxial with the solenoid and in a plane perpendicular to the axis, is made of two resistors joined at diametrically opposite points P (at the top of the view) and Q (at the bottom): a 220Ω resistor forms the right-hand half of the ring and a 680Ω resistor the left-hand half. The connecting wire has negligible resistance.
((a)) Explain why the current that appears in this stationary ring cannot be driven by a magnetic force on its carriers, and, using a circular path coaxial with the solenoid together with the symmetry of the arrangement, derive the magnitude of the induced electric field at a radius s<R. Evaluate it at the solenoid's surface, s=R.
((b)) Find the emf round the ring, and the current in it, stating its sense in the view described.
((c)) Two ideal voltmeters (drawing no current) are each connected to P and Q with the + lead on P. The leads of the first run close alongside the right-hand (220Ω) half of the ring, those of the second close alongside the left-hand (680Ω) half, so that in each case the loop formed by meter, leads and that half of the ring encloses negligible flux from the solenoid. Give the signed reading VP−VQ of each meter, show that the two readings differ by the emf, and say what this proves about the induced field.