920_Physics ProblemsTechnical Physics - 260 Inductance 2U(a It has a magnetic field and it stores energy so L =(b Every field line goes through the

260 Inductance P32.75 (a) It has a magnetic field, and it stores energy, so L U I = 2 2 is non-zero. (b) Every field line goes through the rectangle between the conductors. (c) Φ = LI so L I I BdA y a w a = = = − z Φ 1 L I xdy I y I w y I Ix y dy x y a w a a w a = + − F H G I K J = = − − z z 1 2 2 2 2 2 2 0 0 0 0 µ π µ π µ π µ π b g ln . Thus L x w a a = − F H G I K J µ π 0 ln . P32.76 For an RL circuit, I t I e R L t a f b g = − max : I t I e R L t R L t a f b g max = − = ≅ − − − 1 10 1 9 R L t = − 10 9 so R max . . . . = × × = × − − − 3 14 10 10 2 50 3 16 10 3 97 10 8 9 7 25 e je j b g e j yr s yr Ω . (If the ring were of purest copper, of diameter 1 cm, and cross-sectional area 1 mm 2 , its resistance would be at least 10 6 − Ω ). P32.77 (a) U LI B = = × = × 1 2 1 2 50 0 50 0 10 6 25 10 2 3 2 10 . . . H A J a f e j (b) Two adjacent turns are parallel wires carrying current in the same direction. Since the loops