Phy 213: General Physics IIIElectromagnetic InductionMagnetic FluxFaraday’s LawChanging Magnetic FieldChanging AreaChanging OrientationLenz’s LawOperating a light bulb with motional EMFForce & Magnetic InductionGenerators & Alternating CurrentMaxwell’s EquationsSignificance of Maxwell’s EquationsPhy 213: General Physics IIIChapter 30: Induction & InductanceLecture NotesElectromagnetic Induction•We have observed that force is exerted on a charge by either and E field or a B field (when charge is moving):•Consequences of the Lorentz Force:–A B field can exert a force on an electric current (moving charge)–A changing B-field (such as a moving magnet) will exert a magnetic force on a static charge, producing an electric current → this is called electromagnetic induction•Faraday’s contribution to this observation:–For a closed loop, a current is induced when:1. The B-field through the loop changes2. The area (A) of the loop changes3. The orientation of B and A changeson a charge{together this is the Lorentz Force}F = qE + qv B �r r rrqvrNSBrFrqvrNSBrFr•A current is induced ONLY when any or all of the above are changing•The magnitude of the induced current depends on the rate of change of 1-3Moving chargeMoving magnetMagnetic Flux•Faraday referred to changes in B field, area and orientation as changes in magnetic flux inside the closed loop•The formal definition of magnetic flux (B(analogous to electric flux)When B is uniform over A, this becomes:•Magnetic flux is a measure of the # of B field lines within a closed area (or in this case a loop or coil of wire)•Changes in B, A and/or  change the magnetic fluxFaraday’s Law: changing magnetic flux induces electromotive force (& thus current) in a closed wire loopB = B dAF ��r rArBrB = BA cosfF �Faraday’s Law•When no voltage source is present, current will flow around a closed loop or coil when an electric field is present parallel to the current flow.•Charge flows due to the presence of electromotive force, or emf () on charge carriers in the coil. The emf is given by:•An E-field is induced along a coil when the magnetic flux changes, producing an emf (). The induced emf is related to:–The number of loops (N) in the coil–The rate at which the magnetic flux is changing inside the loop(s), orNote: magnetic flux changes when either the magnetic field (B), the area (A) or the orientation (cos ) of the loop changes: ( )d d = E d = -N = -N BA cosdt dtBe fF� ��rrl�ddB=A cosdt dtBfF�d dA=B cosdt dtBfF�( )d cosd=BAdt dtBfF�coil = E d = iRe ��rrl�dsrEriChanging Magnetic FielddB-NA cosdte f= � �A magnet moves toward a loop of wire (N=10 & A is 0.02 m2). During the movement, B changes from is 0.0 T to 1.5 T in 3 s (Rloop is 2  ).1) What is the induced  in the loop?2) What is the induced current in the loop?Changing AreaA loop of wire (N=10) contracts from 0.03 m2 to 0.01 m2 in 0.5 s, where B is 0.5 T and  is 0o (Rloop is 1  ).dA-NB cosdte f= � �1) What is the induced  in the loop?2) What is the induced current in the loop?Changing OrientationA loop of wire (N=10) rotates from 0o to 90o in 1.5 s, B is 0.5 T and A is 0.02 m2 (Rloop is 2  ).1) What is the average angular frequency,  ?2) What is the induced  in the loop?3) What is the induced current in the loop?( )( )d cos-NABdtd cos ωt-NABrdtofee= �= �Lenz’s Law•When the magnetic flux changes within a loop of wire, the induced current resists the changing flux•The direction of the induced current always produces a magnetic field that resists the change in magnetic flux (blue arrows)•Review the previous examples and determine the direction of the currentBrMagnetic flux, BBrIncreasing BiBrIncreasing BiOperating a light bulb with motional EMFConsider a rectangular loop placed within a magnetic field, with a moveable rail (Rloop= 2 ).B = 0.5 Tv = 10 m/sL = 1.0 mQuestions:1) What is the area of the loop?2) How does the area vary with v?3) What is the induced  in the loop?4) What is the induced current in the loop?5) What is the direction of the current?Force & Magnetic InductionWhat about the force applied by the hand to keep the rail moving?•The moving rail induces an electric current and also produces power to drive the current:P = .i = (5 V)(2.5 A) = 12.5 W•The power (rate of work performed) comes from the effort of the hand to push the rail–Since v is constant, the magnetic field exerts a resistive force on the rail:The force of the hand can be determined from the power:Net hand B hand BF = F + F = 0 or F = Fr r r r rhand handPP = F v F = v� �r rrrhand Bms12.5 WF = = 12.5 N =F10r rBFrhandFrGenerators & Alternating Current•Generators are devices that utilize electromagnetic induction to produce electricity•Generators convert mechanical energy into electrical energy–Mechanical energy is utilized to either:•Rotate a magnet inside a wire coil•Rotate a wire coil inside a magnetic field–In both cases, the magnetic flux inside the coil changes producing an induced voltage–As the magnet or coil rotates, it produces an alternating current (AC) {due to the changing orientation of the coil and the magnetic field}•Motors and Generators are equivalent devices–A generator is a motor running in reverse:Maxwell’s EquationsTaken in combination, the electromagnetic equations are referred to as Maxwell’s Equations:1. Gauss’ Law (E)2. Gauss’ Law (B)3. Ampere’s Law4. Faraday’s Lawenco oρdVqE dA = = e e���r rB dA = 0��r ro enc o o odq dB d = i = = E dA dt dtm m me� �� �r r rrl�o oEB d = dAtme�� � ��� �rr rrl�BddE d = - =- B dAdt dtF� �� �r r rrl�BE d = - dAt�� � ��� �rr rrl�Significance of Maxwell’s Equations1. A time changing E field induces a B field. 2. A time changing B field induces an E field. 3. Together, 1 & 2 explain all electromagnetic behavior (in a classical sense) AND suggest that both E & B propagate as traveling waves, directed perpendicular to each other AND the propagation of the waves, where:andThe product, oo, has special significance:or22o o2EE = tme���rrr22o o2EE = tme���rrr22o o2BB = tme���rrr8mwaveso o1v = = 2.99x10 = cmeo omeo omeo o2wave1 =