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Physics ys cs 132: 3 Lecture ectu e 22 Elements of Physics II A Agenda d for f T Today d Lenz’ Law Emf opposes change in flux Faraday’s Law Induced EMF in a conducting loop Physics 202: Lecture 10, Pg 1 Lenz’s Law Physics 202: Lecture 10, Pg 2 Lenz’s Law Pushing the bar magnet into the loop causes the magnetic flux to increase in th d the downward d di direction. ti To oppose the change in flux which is what Lenz’s flux, Lenz s law requires, the loop itself needs to generate an upward-pointing upward pointing magnetic field. The induced current ceases as soon as the magnet stops moving. Physics 202: Lecture 10, Pg 3 Lenz’s Law Reasoning Strategy 1. What direction is the magnetic flux that penetrates the coil. 2. Determine whether the magnetic flux that penetrates the coil is increasing or decreasing. Increasing: induced b-field opposes magnetic flux Decreasing: induced b-field alligned with magnetic flux 3. Use RHR-2 to determine the direction of the induced current. Physics 202: Lecture 10, Pg 4 Lenz’s Law Physics 202: Lecture 10, Pg 5 Give it a try: y The current in the straight wire is decreasing. Which is true? A. B B. C. There is a clockwise induced current in the loop. There is a counterclockwise induced current in the loop. There is no induced current in the loop loop. Physics 202: Lecture 10, Pg 6 Lenz’s Law Physics 202: Lecture 10, Pg 7 Lenz’s Lenz s Law Physics 202: Lecture 10, Pg 8 Lenz’s Law Physics 202: Lecture 10, Pg 9 Lenz’s Lenz s Law Physics 202: Lecture 10, Pg 10 Lenz’s Law Physics 202: Lecture 10, Pg 11 Lenz’s Law Physics 202: Lecture 10, Pg 12 Faraday’s Law An emf is induced in a conducting loop if the magnetic flux through the loop changes changes. The magnitude of the emf is: The direction of the emf is such as to drive an induced current in the direction given by Lenz’s law. Physics 202: Lecture 10, Pg 13 Faraday’s Law (Magnitude) Emf = Change in magnetic Flux/Time f i tf ti t Since = B A cos() 3 things can change 1. Area of loop 2. Magnetic field B 3. Angle g between A and B,, Lenz’ Law (Direction) E f opposes change Emf h iin flflux Physics 202: Lecture 10, Pg 14 Using Faraday’s Law If we slide a conducting wire along a U-shaped conducting rail, we can complete a circuit and drive an electric current. We can find the induced emf and current by using F d ’ llaw and Faraday’s d Oh Ohm’s ’ law: Physics 202: Lecture 10, Pg 15 Give it a try: Th induced The i d d emff around d thi this lloop iis A. 200 V. V B. 50 V. C. 2 V. V D. 0.5 V. E. 0 02 V. 0.02 V Physics 202: Lecture 10, Pg 16 Give it a try: A flat at coil co o of wire e has as a resistance es sta ce R=10 0 . Att time t e t=0, it is oriented so the area vector makes an angle 0=30o w.r.t. a constant magnetic field of 0.12 T. The loop is rotated to an angle of 0o in 0.5 seconds. Calculate the induced emf. (a) (b) (c) (d) (e) 2.36 2 36 x 10-33 V 5.35 x 10-3 V 1.92 x 10-3 V 9.36 x 10-3 V 8.33 x 10-3 V Physics 202: Lecture 10, Pg 17 Change A flat coil of wire has a resistance R=10 . At time t=0, t=0 it is oriented so the area vector makes an angle 0=30o w.r.t. a constant magnetic field of 0.12 T. The loop is rotated to an angle of 0o in 0 0.5 5 seconds seconds. Calculate the induced emf. emf i = B A cos(30) f = B A cos(0) f i BA (cos( 0) cos(30)) 0 .5 t tf ti = 1.93 x 10-3 Volts Physics 202: Lecture 10, Pg 18 Give it a try: A flat at coil co o of wire e has as a resistance es sta ce R=10 0 . Att time t e t=0, it is oriented so the normal makes an angle 0=30o w.r.t. a constant magnetic field of 0.12 T. The loop is rotated to an angle of 0o in 0.5 seconds. What direction will current flow? At the instant shown, an induced current in the loop will (a) flow clockwise. (b) flow counterclockwise. (c) not flow. Physics 202: Lecture 10, Pg 19