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**Unformatted text preview: **F-1 Faraday's Law Faraday's Law is one of 4 basic equations of the theory of electromagnetism, called Maxwell's Equations. We have said before that charges makes electric fields. (Gauss's Law) currents make magnetic fields. (Ampere's Law) This is the truth, but not the whole truth. Michael Faraday (British physicist, c.1850) showed that there is a second way to make an electric field: a changing magnetic field makes an electric field. (Faraday's Law) Around 1860, James Maxwell(Scottish physicist) showed that there is a second way to make a magnetic field: a changing electric field makes an magnetic field. (modification of Ampere's Law) Before stating Faraday's Law, we must define some new terms: Definition: emf , E , is (roughly speaking) a voltage difference ( V = E d ) capable of doing continuous useful work.. Think of emf as a battery voltage . Batteries have an emf, but resistors do not, even though a resistor R can have a voltage difference across it ( V = I R ) Technically, the emf around a closed loop L is defined as E d = K K A v L E Recall that voltage difference was defined as B A V E dr = K K . For the case of E-fields created by charges, the voltage difference when we go around a closed loop is zero, since voltage depends only on position, not on path: A A V E dr = = K K Definition: magnetic flux through some surface S, B S if const and A flat B dA B A BAcos Φ = = = θ K K K K B Units [ Φ ] = T m 2 = weber (Wb) B cos θ B θ A area A Last update: 10/30/2009 Dubson Phys1120 Notes, © University of Colorado F-2 Faraday's Law (in words): An induced emf ( E ) is created by changing magnetic flux. Faraday's Law (in symbols): M (1 loop) d d t Φ = E If B = constant emf = E = 0 If B is changing with time d d t Φ = E . If have several loops, (N loops) d N d t Φ = E loop of wire V We can change the magnetic flux Φ in several ways: 1) change B (increase or decrease magnitude of magnetic field) 2) change A (by altering shape of the loop) 3) change the angle θ between B and the area vector A (by rotating the loop, say) Example of Faraday's Law: We have a square wire loop of area A = 10 cm × 10 cm, perpendicular to a magnetic field B which is increasing at a rate d B 0.1T /s d t = + . What is the magnitude of the emf E induced in the loop? ...

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