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UVA PHYS 632 - Lecture 10 Induction and Inductance Ch. 30

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Lecture 10 Induction and Inductance Ch. 30IntroductionFaraday’s LawFirst a Reminder in how to find the Magnetic flux across an areaPowerPoint PresentationMore on Lenz’s Law: An induced current has a direction such that the magnetic field due to the current opposes the change in the magnetic flux that induces the currentSlide 8Demo:Demo: Jumping aluminum ring from core of solenoid powered by an AC source. Press the button.Moving bar of length L and width W entirely immersed in a magnetic field B. In this case an Emf is produced but no current flowsSlide 12Slide 13Motional Emf : Work doneEddy CurrentsEddy Currents DemoDemo: Copper pipe and neodymium-iron-boron magnet with magnetic dipole momentDemo: Hanging aluminum ring with gray magnetSlide 19We can now say that a changing magnetic field produces an electric field not just an Emf. For example:Summary Characteristics of the induced emfExample:Example with numbersWhat is an inductor?What is inductance? What is a Henry?Slide 26Numerical ExampleSlide 28Slide 29How is the magnetic energy stored in a solenoid or coil in our circuit?What is the magnetic energy stored in a solenoid or coilWhat is Mutual Inductance? MSlide 33Lecture 10 Induction and Inductance Ch. 30•Cartoon - Faraday Induction•Opening Demo - Thrust bar magnet through coil and measure the current•Warm-up problem•Topics– Faraday’s Law– Lenz’s Law– Motional Emf–Eddy Currents–Self and mutual induction•Demos Thrust bar magnet through coil and measure the current in galvanometer. Increase number of coils Compare simple electric circuit- light bulb and battery with bar magnet and coil.  Coil connected to AC source will induce current to light up bulb in second coil. Gray magnet, solenoid, and two LED’s, push and pull, shows that different LED’s light up. Lenz’s Law Hanging aluminum ring with gray magnet. Lenz’s Law Jumping aluminum ring from core of solenoid powered by an AC source. Press the button. Slowing down of swinging copper pendulum between poles faces of a magnet. Eddy Currents Two large copper disks with two magnets Neodymium magnet swinging over copper strip. Eddy currents Neodymium magnet falling through copper pipe. Cool with liquid nitrogen. Eddy currents Inductive spark after turning off electromagnet. Inductance.IntroductionStationary charges cause electric fields (Coulombs Law, Gauss’ Law).Moving charges or currents cause magnetic fields (Biot-Savart Law). Therefore, electric fields produce magnetic fields.Question: Can changing magnetic fields cause electric fields?Faraday’s Law•Discovered in 1830s by Michael Faraday and Joseph Henry. Faraday was a poor boy and worked as a lab assistant and eventually took over the laboratory from his boss.•Faraday’s Law says that when magnetic flux changes in time, an Emf is induced in the environment which is not localized and also is non-conservative.•Lets look at various ways we can change the magnetic field with time and induce an Emf. If a conductor is present, a current can be induced.€ Emf = −dφmdt1. What is magnetic flux ?φm2. What is an induced Emf ?First a Reminder in how to find the Magnetic flux across an areaMagnetic fluxBAm=•φ∫⋅=• dAnBmˆrφArea ABdAnBmˆ⋅=•rφAdBrr⋅=dAB θcos=nˆBBnˆUnits:B is in TA is in m2 is in (Webers) WbφmMagnetic flux∫⋅= dAnBˆrφBar magnet fieldFaraday’s Law€ Emf = −dφdtExperiment 1 Thrusting a bar magnet through a loop of wireCurrent flows in the ring and produces a different B field.RiB20μ=at centerProduced by current flowing in the wire.The current flows in the wire to produce a magnetic field that opposes the bar magnet. Note North poles repel each other.Lenz’s LawLenz’s LawB produced by bar magnetMore on Lenz’s Law: An induced current has a direction such that the magnetic field due to the current opposes the change in themagnetic flux that induces the currentQuestion: What is the direction of the current induced in the ring given B increasing or decreasing?B due to induced current B due to induced currentDemo: Gray magnet, solenoid, LEDsPush magnet in, one LED lightsPull magnet out, the other LED lightsNmagnet solenoid<=> repelDemo:Coil connected to AC sourceLight bulb connected to second coil(same as solenoid)Shows how flux changing through one coil due to alternating current induces current in second coil to light up bulb. Note no mechanical motion here.Coil 1Coil 2Iron core (soft)means lots of inductance in wire so AC doesn’t heat up wire.Demo: Jumping aluminum ring from core of solenoid powered by an AC source. Press the button.•When I turn on the current, B is directed upward and momentarily the top of the iron is the North pole. If the ring surrounds the iron, then the flux in it increases in the upward direction. This change in flux increases a current in the ring so as to cause a downward B field opposing that due to the solenoid and iron. This means the ring acts like a magnet with a North pole downward and is repelled from the fixed coil.•Try a square-shaped conductor•Try a ring with a gap in it•Try a ring cooled down to 78 KCoilIron core (soft)NAC sourceinduced currentinduced B fieldRepulsive force because 2 North polesNMoving bar of length L and width W entirely immersed in a magnetic field B. In this case an Emf is produced but no current flows€ ×€ ×€ ×€ ×-vF+vFLBPositive charges pile up at the top and negative charges at the bottom and no current flows, but an Emf is produced. Now let’s complete the circuit.WExperiment 3: Motional Emf Pull a conducting bar in a magnetic field. What happens to the free charges in the material?qvBLemfqUqvBLWork=×==BqvFm×=€ emf = −dφmdt= −BdAdtPull the rectangular loop out of the magnetic field. A current i will be induced to flow in the loop in the direction shown. It produces a magnetic field that tries to increase the flux through the loop.Motional EmfWhat force is required to keep current flowing in the circuit?Uniform magnetic field into the screenA= area of magnetic fieldenclosed by the wireFAWire+ vClose up of the wireBqvFm×=BiLF ×=1€ emf = −dφmdr= −BdAdt= −Bd(Lx)dt= −BLdxdt= −BLvcancelR is the resistanceUniform magnetic field into the screen€ F1=B2L2vRThis is the force you need to pull at to achieve constant speed v.Motional Emf ContinuedF1=FAFABiLF ×=12321FFBixFBiLF−===RBLviiRBLviRemf===Motional Emf : Work doneHow much work am


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UVA PHYS 632 - Lecture 10 Induction and Inductance Ch. 30

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