Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Mathematics of radio engineering wikipedia , lookup
Wien bridge oscillator wikipedia , lookup
Phase-locked loop wikipedia , lookup
Direction finding wikipedia , lookup
Giant magnetoresistance wikipedia , lookup
Magnetic core wikipedia , lookup
Superconductivity wikipedia , lookup
Physics 2102 Spring 2007 Jonathan Dowling Lecture 25: MON 16 MAR Ch30.1–4 Induction and Inductance QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. Fender Stratocaster Solenoid Pickup QuickTime™ and a decompressor are needed to see this picture. 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 QuickTime™ and a YUV420 codec decompressor are needed to see this picture. No Current When Magnet Stops QuickTime™ and a YUV420 codec decompressor are needed to see this picture. loop 1 loop 2 In the figure we show a second type of experiment 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. The Current in Loop One Produces a Rapidly Changing QuickTime™ and a Magnetic Field in Cinepak decompressor Loop Two That are needed to see this picture. Induces a Current in Loop One Loop Two — Lighting Has a 60 Hz the Bulb! Alternating Current QuickTime™ and a Cinepak decompressor are needed to see this picture. • Faraday’s Law: What? The Flux! r A time varying magnetic B dA FLUX creates an induced EMF • Definition of magnetic flux is similar to definition of electric flux r r B B dA S EEMF dB 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 W. r dA B 300 60° r r B B dA • What is the induced current? Is it …clockwise or …counterclockwise? BA cos(600 ) BA /2 dB A dB E dt 2 dt E A dB i R 2R dt (1m2 ) i (1T/s) 0.05A 2(10W) 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 rate. • III encloses no flux so EMF=0 • Rank the 3 loops in order of • I and II enclose same flux so EMF same. increasing induced EMF. • Are Currents in Loops I & II – (a) III < II < I ? Clockwise or Counterclockwise? – (b) III < II = I ? – (c) III = II = I ? Example B 0i 2r i • An infinitely long wire carries a constant current i as shown R r=R+x • A square loop of side L is moving x L dR/dt=v towards the wire with a constant velocity L v. • What is the EMF induced in the loop Choose a “strip” of width dx when it is a distance R from the loop? located as shown. Flux thru this “strip” B L 0 0iLdx 2 (R x) 0iLdx d BLdx 2 (R x) 0iL ln( R x) 2 0 0iL R L ln 2 R L dB E dt 0 Li d ln 1 2 dt L R Example dB 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. r r B B dA S t f 2 L B B BL cos( ) dB 2 d E BL sin( ) BL2 2f sin( 2ft) 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? QuickTime™ and a H.264 decompressor are needed to see this picture. 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!! QuickTime™ and a H.264 decompressor are needed to see this picture.