DOC PREVIEW
LSU PHYS 2102 - Induction and Inductance

This preview shows page 1-2-3-4-5-6 out of 18 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 18 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 18 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 18 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 18 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 18 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 18 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 18 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

Physics 2102 Spring 2007 Lecture 17PowerPoint PresentationFaraday’s LawExampleExampleSlide 6Slide 7Example (continued)Example : the GeneratorExample: Eddy CurrentsAnother Experimental ObservationSome interesting applicationsExample : the ignition coilAnother formulation of Faraday’s LawSlide 15Slide 16Slide 17SummaryPhysics 2102 Spring 2007Physics 2102 Spring 2007Lecture 17Lecture 17Ch30:Ch30: Induction and Inductance IInduction and Inductance IPhysics 2102Spring 2007Jonathan DowlingQuickTime™ and a decompressorare needed to see this picture.dAFaraday’s LawFaraday’s Law•A time varying magnetic FLUX creates an induced EMF•Definition of magnetic flux is similar to definition of electric flux BndtdEMFBΦ−=∫⋅=ΦSBdAnB)r• 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”).Example Example •When the N pole approaches the loop, the flux “into” the loop (“downwards”) increases•The loop can “oppose” this change if a current were to flow clockwise, hence creating a magnetic flux “upwards.”•So, the induced EMF is in a direction that makes a current flow clockwise. •If the N pole moves AWAY, the flux “downwards” DECREASES, so the loop has a counter clockwise current!ExampleExample•A closed loop of wire encloses an area of 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 1T/s. The resistance of the wire is 10 .•What is the induced current?∫⋅=ΦSBdAnB)r2)60cos(0BABA ==dtdBAdtdEMFB2=Φ=dtdBRAREMFi2==AsTmi 05.0)/1()10(2)1(2=Ω=300nIs it …clockwise or …counterclockwise?Example Example •3 loops are shown.•B = 0 everywhere except in the circular region where B is uniform, pointing out of the page and is increasing at a steady rate.•Rank the 3 loops in order of increasing induced EMF.–(a) III, II, I–(b) III, (I & II are same)–(c) ALL SAME.IIIIII• Just look at the rate of change of ENCLOSED flux• III encloses no flux and it does not change.• I and II enclose same flux and it changes at same rate.Example 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?LLv∫+=ΦLBxRdxiL00)(2)(πμLxRiL00)ln(2⎥⎦⎤⎢⎣⎡+=πμ⎥⎦⎤⎢⎣⎡+=RLRiLln20πμChoose a “strip” of width dx located as shown.Flux thru this “strip” )(2)()(0xRdxiLdxBL+==πμ⎭⎬⎫⎩⎨⎧⎥⎦⎤⎢⎣⎡+−=Φ−=RLdtdLidtdEMFB1ln20πμRxExample (continued)Example (continued)dtdEMFBΦ−=⎭⎬⎫⎩⎨⎧⎥⎦⎤⎢⎣⎡+−=RLdtdLi1ln20πμ202 RLLRRdtdRLi⎥⎦⎤⎢⎣⎡+=πμ⎥⎦⎤⎢⎣⎡+=RLRLvi)(220πμLvRxWhat 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.Example : the GeneratorExample : 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.BLB∫⋅=ΦSBdAnB)r)cos(2θBL=)sin(2θθdtdBLdtdEMFB=Φ−=( ))2sin(22ftfBL ππ=Example: Eddy CurrentsExample: 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 ObservationAnother Experimental Observation•Drop a non-magnetic pendulum (copper or aluminum) through an inhomogeneous magnetic field•What do you observe? Why? (Think about energy conservation!)N SPendulum had kinetic energyWhat happened to it?Isn’t energy conserved??Some interesting applicationsSome interesting applicationsMagLev train relies on Faraday’s Law: currents induced in non-magnetic rail tracks repel the moving magnets creating the induction; result: levitation! Guitar pickups also use Faraday’s Law -- a vibrating string modulates the flux through a coil hence creating an electrical signal at the same frequency.Example : the ignition coilExample : the ignition coil•The gap between the spark plug in a combustion engine needs an electric field of ~107 V/m in order to ignite the air-fuel mixture. For a typical spark plug gap, one needs to generate a potential difference > 104 V!•But, the typical EMF of a car battery is 12 V. So, how does a spark plug work??spark12VThe “ignition coil” is a double layer solenoid:• Primary: small number of turns -- 12 V• Secondary: MANY turns -- spark plughttp://www.familycar.com/Classroom/ignition.htm•Breaking the circuit changes the current through “primary coil”• Result: LARGE change in flux thru secondary -- large induced EMF!dAAnother formulation of Another formulation of Faraday’s LawFaraday’s Law•We saw that a time varying magnetic FLUX creates an induced EMF in a wire, exhibited as a current.•Recall that a current flows in a conductor because of electric field.•Hence, a time varying magnetic flux must induce an ELECTRIC FIELD!•Closed electric field lines!!?? No potential!! BndtdsdEBCΦ−=⋅∫rrAnother of Maxwell’s equations!To decide SIGN of flux, use right hand rule: curl fingers around loop, +flux -- thumb.ExampleExample •The figure shows two circular regions R1 & R2 with radii r1 = 1m & r2 = 2m. In R1, the magnetic field B1 points out of the page. In R2, the magnetic field B2 points into the page. •Both fields are uniform and are DECREASING at the SAME steady rate = 1 T/s.•Calculate the “Faraday” integral for the two paths shown.R1R2∫⋅CsdErrIIIVsTrdtdsdEBC14.3)/1)((21+=−−=Φ−=⋅∫πrrPath I:[ ]VsTrsTrsdEC42.9)/1)(()/1)((2221+=−+−−−=⋅∫ππrrPath II:Example Example •A long solenoid has a circular cross-section of radius R.•The current through the solenoid is increasing at a steady rate di/dt.•Compute the variation of the electric field as a function of the distance r from the axis of the solenoid. RFirst, let’s look at r < R:dtdBrrE )()2(2ππ =dtdBrE2=Next, let’s look at r > R:dtdBRrE )()2(2ππ =dtdBrRE22=magnetic field lineselectric field linesExample


View Full Document

LSU PHYS 2102 - Induction and Inductance

Documents in this Course
Load more
Download Induction and Inductance
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Induction and Inductance and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Induction and Inductance 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?