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Physics 2102 Lecture 18

Physics 2102 Jonathan Dowling. Physics 2102 Lecture 18. Ch30: Inductors & Inductance II. Nikolai Tesla. n. 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!!

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Physics 2102 Lecture 18

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  1. Physics 2102 Jonathan Dowling Physics 2102 Lecture 18 Ch30: Inductors & Inductance II Nikolai Tesla

  2. n 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”).

  3. n dA Another formulation of Faraday’s Law 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 the forces on charges produced by an electric field. • Hence, a time varying magnetic flux must induce an ELECTRIC FIELD! • But the electric field line would be closed!!?? What about electric potential difference DV=∫E•ds? Another of Maxwell’s equations! To decide SIGN of flux, use right hand rule: curl fingers around loop C, thumb indicates direction for dA.

  4. magnetic field lines electric field lines Example R 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 electric field as a function of the distance r from the axis of the solenoid. The electric current produces a magnetic field B=m0ni, which changes with time, and produces an electric field.The magnetic flux through circular disks F=∫BdA is related to the circulation of the electric field on the circumference ∫Eds. First, let’s look at r < R: Next, let’s look at r > R:

  5. magnetic field lines E(r) r r = R electric field lines Example (continued)

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

  7. Using Faraday’s law: Joseph Henry (1799-1878) Inductors: Solenoids Inductors are with respect to the magnetic field what capacitors are with respect to the electric field. They “pack a lot of field in a small region”. Also, the higher the current, the higher the magnetic field they produce. Capacitance how much potential for a given charge: Q=CV Inductance how much magnetic flux for a given current: F=Li

  8. i L = “inductance” “Self”-Inductance of a solenoid • Solenoid of cross-sectional area A, length l, total number of turns N, turns per unit length n • Field inside solenoid = m0 n i • Field outside ~ 0

  9. i (a) 50 V (b) 50 V Example • The current in a 10 H inductor is decreasing at a steady rate of 5 A/s. • If the current is as shown at some instant in time, what is the magnitude and direction of the induced EMF? • Magnitude = (10 H)(5 A/s) = 50 V • Current is decreasing • Induced emf must be in a direction that OPPOSES this change. • So, induced emf must be in same direction as current

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