Solutions to Additional Conceptual Practice Problems for PHYS 1112 Final Exam

Physics 1112Spring 2009University of GeorgiaInstructor: HBSchüttlerDetailed Problem Statement:A bar magnet is moved either towards or away from a circular conducting ring with eitherits north-pole (N) or its south-pole (S) pointing towards the ring, and the respective polebeing located either above the plane of the ring (in ”Top” position ”T”) or below the planeof the ring (in ”Bottom” position ”B”), as shown in the Fig. As also shown in Fig., theplane of the ring defines the x-y-plane, and the magnet’s N-S-axis is oriented parallel to thez-axis while the magnet is being moved.Which of the five motion processes of the bar magnet, (A)-(E) described above, will inducea clockwise (cw) current I in the ring?Solution:Above/below the poles of the bar magnet, ⃗ B points approximately along the z-axis, outof the N- and into the S-pole, with the field strength B ≡ | ⃗ B| decreasing with increasingdistance from either pole.Hence, the magnetic field ⃗ B inside the ring points in +z-direction when the N-pole is belowthe ring pointing up (in Bottom position ”B”) or when the S-pole is above the ring pointingdown (in Top position ”T”). Likewise, ⃗ B inside the ring points in −z-direction when theS-pole is below the ring pointing up (in Bottom position ”B”) or when the N-pole is abovethe ring pointing down (in Top position ”T”). Also, the field strength B inside the ringincreases if either pole is moving towards the ring; and the field strength B inside the ringdecreases if either pole is moving away from the ring.By Lenz’s rule, the induced current I in the ring produces a secondary field, ⃗ BI , whichopposes the change ∆ ⃗ B of the time-dependent inducing field ⃗ B(t). Also, the direction of I isrelated to the ⃗ B I -direction by a right-hand (RH) rule: if RH thumb is in direction of ⃗ B I , theRH 4 fingers point in the flow direction of I. So, to produce a ⃗ B I pointing in −z-directionrequires a clockwise I, as defined in Fig.; to produce a ⃗ B I pointing in +z-direction requiresa counter-clockwise I.Hence, ∆ ⃗ B points in +z-direction, and by Lenz’s rule, ⃗ B I points in −z-direction, and I flowsclockwise ifCase (1): ⃗ B points in +z-direction and its strength B increases in magnitude; orCase (2): ⃗ B points in −z-direction and its strength B decreases in magnitude.Likewise, ∆ ⃗ B points in −z-direction, and by Lenz’s rule, ⃗ B I points in +z-direction, and Iflows counter-clockwise ifCase (3): ⃗ B points in +z-direction and its strength B decreases in magnitude; orCase (4): ⃗ B points in −z-direction and its strength B increases in magnitude.Thus, in the answer key above, process (A) corresponds to Case (1), process (B) correspondsto Case (3), process (C) corresponds to Case (4), process (D) corresponds to Case (4), andprocess (E) corresponds to Case (3). So, only process (A) induces a clockwise current, while(B), (C), (D) and (E) all induce a counter-clockwise current in the ring.2