Physics 2102 Jonathan Dowling Lecture 18 TUE 23 MAR 2010 Ch30 1 4 Induction and Inductance I Fender Stratocaster Solenoid Pickup http www phys lsu edu classes spring2010 phys2102 exam2solutions pdf EXAM II AVG 65 100 APPROXIMATE CURVE A 100 90 B 89 80 C 79 50 D 49 45 F 44 0 Faraday s Experiments In a series of experiments Michael Faraday in England and Joseph Henry in the U S were able to generate electric currents without the use of batteries The circuit shown in the figure consists of a wire loop connected to a sensitive ammeter known as a galvanometer If we approach the loop with a permanent magnet we see a current being registered by the galvanometer 1 A current appears only if there is relative motion between the magnet and the loop 2 Faster motion results in a larger current 3 If we reverse the direction of motion or the polarity of the magnet the current reverses sign and flows in the opposite direction The current generated is known as induced current the emf that appears is known as induced emf the whole effect is called induction Changing B Field Induces a Current in a Wire Loop Note Current Changes Sign With Direction No Current When Magnet Stops In the figure we show a second type of experiment loop 1 loop 2 in which current is induced in loop 2 when the switch S in loop 1 is either closed or opened When the current in loop 1 is constant no induced current is observed in loop 2 The conclusion is that the magnetic field in an induction experiment can be generated either by a permanent magnet or by an electric current in a coil Faraday summarized the results of his experiments in what is known as Faraday s law of induction An emf is induced in a loop when the number of magnetic field lines that pass through the loop is changing Loop Two is Connected To A Light Bulb Loop One Has a 60 Hz Alternating Current The Current in Loop One Produces a Rapidly Changing Magnetic Field in Loop Two That Induces a Current in Loop Two Lighting the Bulb Faraday s Law What The Flux A time varying magnetic B dA FLUX creates an induced EMF Definition of magnetic flux is similar to definition of electric flux B B dA S E EMF d B dt dA Take note of the MINUS sign The induced EMF acts in such a way that it OPPOSES the change in magnetic flux Lenz s Law Lenz s Law The Loop Current Produces a B Field that Opposes the CHANGE in the bar magnet field Upper Drawing B Field from Magnet is INCREASING so Loop Current is Clockwise and Produces an Opposing B Field that Tries to CANCEL the INCREASING Magnet Field Lower Drawing B Field from Magnet is DECREASING so Loop Current is Counterclockwise and Tries to BOOST the Decreasing Magnet Field Example A closed loop of wire encloses an area of A 1 m2 in which in a uniform magnetic field exists at 300 to the PLANE of the loop The magnetic field is DECREASING at a rate of dB dt 1T s The resistance of the wire is 10 What is the induced current Is it clockwise or counterclockwise dA B 300 60 B B dA BAcos 60 0 BA 2 E d B A dB dt 2 dt E A dB i R 2R dt 1m2 1T s 0 05A i 2 10 Example 3 loops are shown B II B 0 everywhere except in III I the circular region I where B is uniform pointing out of the page and is increasing at a steady III encloses no flux so EMF 0 rate I and II enclose same flux so EMF same Rank the 3 loops in order of increasing induced EMF Are Currents in Loops I II Clockwise or Counterclockwise a III II I b III II I c III II I Example An infinitely long wire carries a constant current i as shown A square loop of side L is moving towards the wire with a constant velocity v What is the EMF induced in the loop when it is a distance R from the loop B L 0 0iLdx 2 R x 0i 2 r i R dR dt v x L r R x L Choose a strip of width dx located as shown Flux thru this strip 0iLdx d BLdx 2 R x L 0iL ln R x 2 0 0iL R L ln 2 R B d B E dt 0 Li d ln 1 2 dt L R Example d B E dt 0 Li d L ln 1 2 dt R 0 Li dR R L 2 dt R L R 2 0i L2 v 2 R L R i R dR dt v L x What is the DIRECTION of the induced current Magnetic field due to wire points INTO page and gets stronger as you get closer to wire So flux into page is INCREASING Hence current induced must be counter clockwise to oppose this increase in flux CCW B Example The Generator A square loop of wire of side L is rotated at a uniform frequency f in the presence of a uniform magnetic field B as shown Describe the EMF induced in the loop B B dA S t f 2 L B B BL cos d B 2 d 2 E BL sin BL 2 f sin 2 ft dt dt 2 Example Eddy Currents A non magnetic e g copper aluminum ring is placed near a solenoid What happens if There is a steady current in the solenoid The current in the solenoid is suddenly changed The ring has a cut in it The ring is extremely cold Another Experimental Observation Drop a non magnetic pendulum copper or aluminum through an inhomogeneous magnetic field What do you observe Why Think about energy conservation Pendulum had kinetic energy What happened to it Isn t energy conserved N S Energy is Dissipated by Resistance P i2R This acts like friction
View Full Document
Unlocking...