Lecture 10 Induction and Inductance Chp. 31Faraday’s LawFirst a Reminder in how to find the Magnetic flux across an areaLenz’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 currentExperiment 2 Throwing the switchA simple example using a solenoid: Find the total magnetic flux through a solenoid with N = 600 turns, length = 0.4 m, radius = 3 cm, and current = 10 A.PowerPoint PresentationDemo: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-born magnetDemo: 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:Characteristics of the induced emfExample:Example with numbersWhat is an inductor?What is inductance? L What is a Henry?Numerical ExampleSlide 27Slide 28How 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 32Warm up set 10 Due 8:00 am TuesdayLecture 10 Induction and Inductance Chp. 31•Cartoon - Faraday Induction•Opening Demo - Thrust bar magnet through coil and measure the current•Warm-up problem•Physlet •Topics–Stationary charges cause electric fields Coulombs Law, Gauss’ Law–Moving charges or currents ie. Electric fields cause magnetic fields- Biot Savart Law–Can changing magnetic fields cause electric fields?–Magnetic flux, Faraday’s Law, Lenz’s Law, Motional Emf, Eddy Currents–Self and mutual induction, Circuit with resistance and inductor, and battery.•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.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 a current.€ Emf = −dφmdtFirst a Reminder in how to find the Magnetic flux across an areaMagnetic fluxBAm=•φ∫⋅=• dAnBmˆrφArea ABdAnBmˆ⋅=•rφAdBrr⋅=dAB θcos=nˆBBnˆMagnetic flux∫⋅= dAnBˆrφBar magnetFaraday’s Law€ Emf = −dφdtRiB20μ=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.Experiment 1 Thrusting a bar magnet through a loop of wireLenz’s LawLenz’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 currentExperiment 2 Throwing the switchIn this case we throw the switch and as the currentIncreases from 0 to some value the magnetic field is changing with time and hence the flux through the second circuit is varying producing an induced Emf in the second circuit causing current to flow.Current in the second circuit only flows when thecurrent in the first circuit changes with time. It stopsflowing when the current in the first circuit is constant.A simple example using a solenoid: Find the total magnetic flux through a solenoid with N = 600 turns, length = 0.4 m, radius = 3 cm, and current = 10 A.o o o o o o o o x x x x x x x x .4BANm=φNrBm2πφ =600)03(.2⋅= πB270.1)54(. mBB ⋅== π€ φm= 0.032 T.m2= 0.032Webe rWeber = T m2Note   N2Flux increases like the square of the number of turns N for a solenoid.N=600 turnsl=0.4mi = 10 AN = 600/0.4m =1500 turns/m€ B = μ0ni€ =4π ×10−71500(10)€ =0.01884 TN/LIncrease B by using an iron coreDemo: 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)NNAC sourceinduced currentinduced B fieldRepulsive force because 2 North polesMoving 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.WWork =qvBLU=q emf =qvBLExperiment 3: Motional Emf Pull a