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Induction and Inductance in Physics

Learn about how changing magnetic fields produce currents, Faraday’s Law, induction applications in MagLev trains and electric guitars, and the workings of an ignition coil. Also explore how changing magnetic fields create induced electric fields and calculate variations in electric fields in solenoids.

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Induction and Inductance in Physics

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  1. Physics 2102 Spring 2007 Jonathan Dowling Lecture 26: WED 18 MAR Ch30.4–6 Induction and Inductance

  2. A Changing Magnetic Field Produces a Current in a Wire Loop

  3. dA Faraday’s Law B • A time varying magnetic FLUX creates an induced EMF • Definition of magnetic flux is similar to definition of electric flux • 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”).

  4. Some Applications MagLev train relies on Faraday’s Law: currents induced in non-magnetic rail tracks repel the moving magnets creating the induction; result: levitation! ELECTRIC 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. Fender Stratocaster Solenoid Pickup

  5. spark 12V http://www.familycar.com/Classroom/ignition.htm Start Your Engines: 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?? • Breaking the circuit changes the current through “primary coil” • Result: LARGE change in flux thru secondary -- large induced EMF! • The “ignition coil” is a double layer solenoid: • Primary: small number of turns -- 12 V • Secondary: MANY turns -- spark plug

  6. Start Your Engines: The Ignition Coil Transformer: P=iV

  7. dA Changing B-Field Produces E-Field! B • 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! • A Changing B-Field Produces an E-Field in Empty Space! To decide SIGN of flux, use right hand rule: curl fingers around loop, +flux -- thumb.

  8. Path I: Path II: Example R2 R1 • 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. B1 I B2 II

  9. magnetic field lines electric field lines Solenoid Example B • A long solenoid has a circular cross-section of radius R. • The magnetic field B through the solenoid is increasing at a steady rate dB/dt. • Compute the variation of the electric field as a function of the distance r from the axis of the solenoid. Next, let’s look at r > R: First, let’s look at r < R:

  10. i i Added Complication: Changing B Field Is Produced by Changing Current i in the Loops of Solenoid! E(r) r r = R Solenoid Example Cont. B E

  11. Summary Two versions of Faradays’ law: • A time varying magnetic flux produces an EMF: • A time varying magnetic flux produces an electric field:

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