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quiz6_sol - PHYSICS 4C QUIZ 6 SOLUTIONS Problem 1 Magnetic...

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PHYSICS 4C: QUIZ 6 SOLUTIONS Problem 1 Magnetic field outside the solenoid is 0 and inside (1) B = μ 0 nI s , where I s is the current through the solenoid. The flux through the coil is (2) Φ B = Bπr 2 s N = πμ 0 nI s r 2 s N. The EMF in the coil is (3) ε = - d Φ B dt = - πμ 0 n ˙ I s r 2 s N = - 0 . 11V . The magnitude of the current is (4) I = ε R = 0 . 74A and the power dissipated is (5) P = I 2 R = 0 . 081W. Problem 2 The current is clockwise because right-hand rule shows that clockwise current creates magnetic field into the page, which would compensate for the increasing magnetic flux. The change of the magnetic flux through the loop is (6) ˙ Φ B = B ˙ A = Bhv. Since the current on the top and bottom sides of the loop is equal and opposite, the force is only result of current in the right segment of the loop. (7) ~ F = I ~ h × ~ B ~ B and ~ h are orthogonal, so (8) I = F hB = 0 . 28A which means the power dissipated is (9) P = I 2 R = 0 . 062W. The EMF is (10) ε = IR = 0 . 22V = - ˙ Φ B = - Bhv. Solving for the magnitude of velocity, (11) v = ε Bh = 0 . 62m/s. 1
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2 PHYSICS 4C: QUIZ 6 SOLUTIONS Problem 3 (12) I = dQ dt = ε R = - 1 R d Φ B dt (13) dQ = - d Φ B R (14) Δ Q = - ΔΦ B R = - πr 2 B R (cos θ f - cos θ i ) = 0 . 014C Problem 4
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