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Lecture 13

# Lecture 13 - Lecture 13 March 2 2010 Chapter 30 Induction...

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Lecture 13 March 2, 2010 Chapter 30 Induction and Inductance

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- Faraday’s law of induction - Lenz’s rule - Electric field induced by a changing magnetic field - Inductance and mutual inductance - RL circuits - Energy stored in a magnetic field (30 1) Outline
In a series of experiments Michael Faraday in England and Joseph Henry in the US were able to generate electric currents without the use of batteries. Below we Faraday's experiments describe some of these experiments that helped formulate whats is known as "Faraday's law of induction" Michael Faraday 1791-1867 Joseph Henry 1997-1878

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The circuit shown in the figure consists of a wire loop connected to a sensitive ammeter (known as a "galvanometer"). If we approach the loop with a permanent magnet we see a current being registered by the galvanometer. The results can be summarized as follows: A current appears only if there is relative motion betwee 1. n the magnet and the loop Faster motion results in a larger current If we reverse the direction of motion or the polarity of the magnet, the current reverses sign and flows in the opposite 2. 3. direction. The current generated is known as " "; the emf that appears is known as " "; the whole effect is called " " induced current induced emf induction
loop 1 loop 2 In the figure we show a second type of experiment in which current is induced in loop 2 when the switch S in loop 1 is either closed or opened. When the current in loop 1 is constant no induced current is observed in loop 2. The conclusion is that the magnetic field in an induction experiment can be generated either by a permanent magnet or by an electric current in a coil.

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Faraday summarized the results of his experiments in what is known as " " Faraday's law of induction An emf is induced in a loop when the number of magnetic field lines that pass through the loop is changing. Faraday's law is not an explanation of induction but merely a description of of what induction is. It is one of the four " of electromagnetism" all of which are statements of experi Maxwell's equations mental results. We have already encountered Gauss' law for the electric field, and Ampere's law (in its incomplete form).
B ˆ n dA The magnetic flux through a surface that borders a loop is determined as follows: we divide the surface that has the loop as its border into area elements of area . dA B Magnetic Flux Φ 1. For each element we calculate the magnetic flux through it: cos ˆ Here is the angle between the normal and the magnetic field vectors at the position of the element. We integrate a B d BdA n B 2. 3. 2 : T m known as the Weber (symbol ll the terms. cos We can express Faraday's law of induction in the folowin W g b) form: B BdA B dA SI magnetic flux unit B The magnitude of the emf induced in a conductive loop is equal to rate at which the magnetic flux Φ through the loop changes with time B B dA B d dt   (30 4)

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B ˆ n dA cos B BdA B dA Change the magnitude of within the loop
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Lecture 13 - Lecture 13 March 2 2010 Chapter 30 Induction...

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