Faraday - F-1 Faraday's Law Faraday's Law is one of 4 basic...

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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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