Ch30.1–4 Induction and Inductance Physics 2102 Spring 2007 Jonathan Dowling Lecture 25: MON 16 MAR Ch30.1–4 Induction and Inductance Fender Stratocaster Solenoid Pickup

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Changing B-Field Induces a Current in a Wire Loop

No Current When Magnet Stops Note Current Changes Sign With Direction No Current When Magnet Stops

loop 1 loop 2

Loop Two is Connected To A Light Bulb. The Current in Loop One Produces a Rapidly Changing Magnetic Field in Loop Two That Induces a Current in Loop Two — Lighting the Bulb! Loop One Has a 60 Hz Alternating Current

Faraday’s Law: What? The Flux! A time varying magnetic FLUX creates an induced EMF Definition of magnetic flux is similar to definition of electric flux B dA 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”).

Lenz’s Law The Loop Current Produces a B Field that Opposes the CHANGE in the bar magnet field. Upper Drawing: B Field from Magnet is INCREASING so Loop Current is Clockwise and Produces an Opposing B Field that Tries to CANCEL the INCREASING Magnet Field Lower Drawing: B Field from Magnet is DECREASING so Loop Current is Counterclockwise and Tries to BOOST the Decreasing Magnet Field.

Example B 300 60° A closed loop of wire encloses an area of A = 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 dB/dt = 1T/s. The resistance of the wire is 10 W. What is the induced current? Is it …clockwise or …counterclockwise?

Example 3 loops are shown. B B = 0 everywhere except in the circular region I 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 < II = I ? (c) III = II = I ? I II III B • III encloses no flux so EMF=0 • I and II enclose same flux so EMF same. Are Currents in Loops I & II Clockwise or Counterclockwise?

Example i 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? R r=R+x x L dR/dt=v L Choose a “strip” of width dx located as shown. Flux thru this “strip”

Example i R B x dR/dt=v L What 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 = CCW

Example : 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. L B B 

Example: 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 Observation Drop a non-magnetic pendulum (copper or aluminum) through an inhomogeneous magnetic field What do you observe? Why? (Think about energy conservation!) Pendulum had kinetic energy What happened to it? Isn’t energy conserved?? Energy is Dissipated by Resistance: P=i2R. This acts like friction!! N S