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Phy2005 Applied Physics II Spring 2017 Announcements: Last Time (& time before last) Faraday’s law: any time there is a time-changing magnetic flux through an area, there is an electromotive force (voltage) tending to drive current around the boundary of the area Vind = - A (dB/dt) rate of ch of B with time = - d/dt (rate of ch of with time) = BA= B A : magnetic flux Sign in Faraday’s law – “Lenz’s law” Current flows in a direction so as to oppose the change in flux it experiences Last time: practice w/ Faraday Magnet always feels resistance to its motion. Demos Earth field generator Faraday’s law with diode Q1. ( 23.7) A flat loop of wire has an area of 0.004 m2. It is in a region where B=0.02 T and directed along the x axis. is the angle between the normal of the loop and the x axis. The loop is rotated from =0o to =60o in 0.5s. What is the change in flux? d = BfA-BiA = BAcos f-BAcos i) = (0.02)(0.004)(1/2 – 1) = -4 x 10-5 T-m2 A. 0 B. -1.1×10-4 V C. 8 x 10-5 T D. -4 x 10-5 T-m2 E. 4 x 10-1 T-m2 B B B ACADEMIC HONESTY Each student is expected to hold himself/herself to a high standard of academic honesty. Under the UF academic honesty policy. Violations of this policy will be dealt with severely. There will be no warnings or exceptions. Q2. ( 23.7) A flat loop of wire has an area of 0.004 m2. It is in a region where B=0.02 T and directed along the x axis. is the angle between the normal of the loop and the x axis. The loop is rotated from =0o to =60o in 0.5s. What is the induced EMF? A. 0 B. 1.1×10-4 V C. 8 x 10-5 V D. 4 x 10-5 V E. 1.1 x 10-1 V B Ex 18-3 A circular loop with a 10 cm-radius is placed in the presence of a uniform magnetic as shown in the figure. The field changes from 1.5 T to 0.5 T in 0.5 s. The loop has resistance 10W. What is the induced EMF? What current flows (specify the direction and magnitude)? . . . . Vind = -d/dt . . . . d = f - I = -0.031 Tm2 . . . . Vind = 0.062 V . . . . . . . . I = Vind/R = 0.0062 Amp Field B out of screen Motional emf L x x x x x x x x x x x x x x x x v x x x x x x x x x x x x x x d i = LdB V dt f = L(d+vdt)B Vind = - d/dt = - LvdtB/dt = - LvB One way to think about it: electrons In wire experience Lorentz force downwards x B - x x x x x x x- x x x - x x x x - - - x x x x x x x x x x x x x x x v Current flows counterclockwise; electrons flow clockwise Vind = - B dA/dt = B (vdt)L/dt = BvL L 23-30 HW challenge: sliding wire (no friction) on inclined rails. Rails are resistanceless, but wire has resistance R. What is the terminal velocity? Q1:Observation: wire slides down, accelerating until it reaches a terminal velocity. Why???? A1: Because induced emf causes counterclockwise current, sliding wire experiences increasing force component up the rails, counteracting gravity Q2: Total mechanical energy not conserved, since KE is const and PE decreasing --- where is energy going? A2: into heat dissipated in the resistor Newton’s 2nd law: balance forces Iind Fwire mg Fwire a Vind lvB cos a l 2 B 2v cos a I ind lB ( )( )lB R R R mgR sin a Fwire cos a mg sin a v 2 2 l B cos 2 a