Solutions to Additional Conceptual Practice Problems for PHYS 1112 Final Exam

Physics 1112Spring 2009University of GeorgiaInstructor: HBSchüttlerof Φ m , with final values of flux Φ ′ m = B ′ A cos Θ ′ , magnetic field strength B ′ and angleΘ ′ ≡ ̸ ( A ⃗′ , B ⃗ ′ ), after changing the field/circuit configuration, as follows:(A) Φ ′ m = −BA < +BA = Φ m with Θ ′ = 180 o and B ′ = B;(B): Φ ′ m = 0 < BA = Φ m with Θ ′ = 90 o and B ′ = B;(C): Φ ′ m = B ′ A < BA = Φ m with Θ ′ = 0 o and B ′ < B;(D): Φ ′ m = BA = Φ m with Θ ′ = 0 o = Θ and B ′ = B;(E): Φ ′ m = B ′ A > BA = Φ m with Θ ′ = 0 o and B ′ > B;(F): Φ ′ m = 0 < BA = Φ m with Θ ′ = 90 o and B ′ = B.Therefore, the time-dependent change of flux ∆Φ m ≡ Φ ′ m − Φ m and the resulting inducedEMF E = −∆Φ m /∆t (with ∆t > 0 here) have the following signs:∆Φ m < 0 and hence E > 0 for processes (A), (B), (C) and (F). By the sign convention forFaraday’s law, a positive EMF E > 0 drives the current I in the loop in right-hand (RH)direction around A ⃗ (i.e., point RH thumb in A-direction; ⃗ then 4 RH fingers will point inI-direction). Since A ⃗ was chosen to point into the paper, ”RH direction around A” ⃗ means:clockwise. So, current I flows clockwise around the loop and therefore deposits positivecharge on the upper capacitor plate (and an equal amount of negative charge on the lowercapacitor plate) in processes (A), (B), (C) and (F).∆Φ m > 0 and hence E < 0 for process (E). By the sign convention for Faraday’s law, anegative EMF E < 0 drives the current I in the loop against RH direction around ⃗ AHence, current I flows counter-clockwise around the loop and therefore deposits negativecharge on the upper capacitor plate (and an equal amount of positive charge on the lowercapacitor plate) in process (E).∆Φ m = 0 and hence E = 0 for process (D). Hence, there is no induced EMF and no inducedcurrent I in the loop and therefore zero charge being deposited on the either capacitor plate.For an alternative way of solving this, using Lenz’s rule, see posted solution of HomeworkProblem P08.01 for details.10