Chapter 29 lecture - Chapter 29 Faraday's Law (Maxwell's...

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Chapter 29 Faraday’s Law (Maxwell’s 3 rd equation) WARNING: Deeply meaningful and mathematically explicit equations will be displayed in this and following lectures. Side effects may include palpitations, fainting, dizziness, rational exuberance, and a deep-seated sense of natural enlightenment. If symptoms persist, remove student to a well ventilated accounting course.
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Experiments with conductors moving in B fields and changing B fields 1. Conductors moving across (cutting) B field lines 2. Magnet moving relative to conducting coil and visa versa Demos Consider the magnetic force on the free conduction charges in a wire that is pulled through the field………………. .
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Motional EMF vBL EL V V V B v E hence B v q E q F bot top net = = = - = × - = × + = = ξ 0 If we complete the circuit so the bar slides on conducting rails we get a current flowing upwards in the bar. We can’t just pull the rigid loop through the field (no current) I So what if there is no relative motion of a conductor cutting through B field lines???
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Changing B fields (with no motion) Demo— Two concentric solenoids with B increasing or decreasing in one-- no conductor motion Darn if we don’t still get induced currents in the other when B changes! We need a more general expression for induced/motional EMF Faraday’s Law (1831) - = Φ - = surf B loop A d B dt d dt d ξ Any closed path Direction of ξ given by Lenz’s Law Any surface bounded by the loop
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Michael Faraday (1791-1867) Faraday quickly recognized the importance of Oersted’s experiment of 1820 and built the first electric motor in 1821. It was not until nearly ten years to the day after his discovery of electro-magnetic rotations that Faraday was able to resume his work on electro-magnetism, when he discovered on 29 August 1831 , electro-magnetic induction. This is the principle behind the electric transformer and generator. It was this discovery, more than any other, that allowed electricity to be turned, during the nineteenth century, from a scientific curiosity into a powerful technology. During the remainder of the 1830s Faraday worked on developing his ideas on electricity. Faraday’s lecture entitled "Thoughts on Ray- vibrations" , delivered in April 1846 , laid the basis for the field theory of electro-magnetism which Faraday developed in the ensuing years. This theory was taken up and mathematised by Thomson, and, at Thomson's instigation, by James Clerk Maxwell in whose hands it became, and remains one of the cornerstones of physics.
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Back to slidewire generator (with bar pulled with v to the right) Question 1: let’s calculate the time derivative of Φ B . If Φ=BxL then dΦ/dt = 1. BxdL/dt 2. Bvdx/dt 3. xLdB/dt 4. BLv x Note that dΦ/dt = BLv = ξ (direction to be worked out) ►►►►same as motional EMF, Faraday’s Law includes the motional EMF effect
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Changing B (with no conductor motion) [ ] loops N for A dt dB N or A dt dB B A dt dB BA dt d dt d loop - = - = - - = - = Φ - = 1 ξ How do we get the direction of induced EMF? 0
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Lenz’s Law
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Chapter 29 lecture - Chapter 29 Faraday's Law (Maxwell's...

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