Lightning Review19.10 Magnetic Field of a current loop19.11 Magnetic Field of a solenoidSolenoid MagnetSolenoid MagnetExample: Magnetic Field inside a Solenoid.Chapter 20Induced EMF and InductionIntroduction20.1 Induced EMF and magnetic fluxProblem: determining a flux20.2 Faraday’s law of inductionDoes there have to be motion?Does there have to be motion?Does there have to be motion?Does there have to be motion?Maybe the B-field needs to change…..Maybe the B-field needs to change…..Maybe the B-field needs to change…..Faraday’s law of magnetic inductionApplications:Example : EMF in a loop1110/7/200310/7/2003General Physics (PHY 2140)Lecture 15Lecture 15¾ Electricity and Magnetism9Magnetism9 Applications of magnetic forces 9Induced voltages and induction9 Magnetic flux and induced emf9 Faraday’s lawChapter 19-20http://www.physics.wayne.edu/~apetrov/PHY2140/2210/7/200310/7/2003Lightning ReviewLightning ReviewsinFBIlθ=Last lecture:1.1.MagnetismMagnetism99Charged particle in a magnetic fieldCharged particle in a magnetic field99Ampere’s law and applicationssinNBIAτθ=mvrqB=02IBrµπ=Ampere’s law and applicationsReview Problem: A rectangular loop is placed in a uniform magnetic field with the plane of the loop parallel to the direction of the field. If a current is made to flow through the loop in the sense shown by the arrows, the field exerts on the loop:1. a net force.2. a net torque.3. a net force and a net torque.4. neither a net force nor a net torque.3310/7/200310/7/200319.10 Magnetic Field of a current loop19.10 Magnetic Field of a current loopMagnetic field produced by a wire can be enhanced Magnetic field produced by a wire can be enhanced by having the wire in a loop.by having the wire in a loop.∆x1BI∆x24410/7/200310/7/200319.11 Magnetic Field of a solenoid19.11 Magnetic Field of a solenoidSolenoid magnet consists of a wire coil with multiple Solenoid magnet consists of a wire coil with multiple loops.loops.It is often called an electromagnet.It is often called an electromagnet.5510/7/200310/7/2003Solenoid MagnetSolenoid MagnetField lines inside a solenoid magnet are parallel, uniformly spaField lines inside a solenoid magnet are parallel, uniformly spaced ced and close together.and close together.The field inside is uniform and strong.The field inside is uniform and strong.The field outside is non uniform and much weaker.The field outside is non uniform and much weaker.One end of the solenoid acts as a north pole, the other as a souOne end of the solenoid acts as a north pole, the other as a south th pole.pole.For a long and tightly looped solenoid, the field inside has a vFor a long and tightly looped solenoid, the field inside has a value:alue:oBnIµ=6610/7/200310/7/2003Solenoid MagnetSolenoid MagnetoBnIµ=n = N/ln = N/l: number of (loop) turns per unit length.: number of (loop) turns per unit length.I I : current in the solenoid.: current in the solenoid.7410 /oTm Aµπ−=×7710/7/200310/7/2003Example: Magnetic Field inside a Solenoid.Example: Magnetic Field inside a Solenoid.Consider a solenoid consisting of 100 turns of wire and Consider a solenoid consisting of 100 turns of wire and length of 10.0 cm. Find the magnetic field inside when it length of 10.0 cm. Find the magnetic field inside when it carries a current of 0.500 A.carries a current of 0.500 A.()()()741001000 /0.104 10 / 1000 / 0.5006.28 10oN turnsn turns mlmBnI TmA turnsm ABTµπ−−== ===×=×N = 100l = 0.100 mI = 0.500 A7410 /oTm Aµπ−=×8810/7/200310/7/2003Comparison:Electric Field vs. Magnetic FieldElectric MagneticSource Charges Moving ChargesActs on Charges Moving ChargesForce F = Eq F = q v B sin(θ)Direction Parallel E Perpendicular to v,BField LinesOpposites Charges Attract Currents Repel9910/7/200310/7/2003Chapter 20Chapter 20Induced EMF and InductionInduced EMF and Induction101010/7/200310/7/2003IntroductionIntroductionPrevious chapter: electric currents produce magnetic Previous chapter: electric currents produce magnetic fields (fields (Oersted’sOersted’sexperiments)experiments)Is the opposite true: can magnetic fields create electric Is the opposite true: can magnetic fields create electric currents?currents?111110/7/200310/7/200320.1 Induced EMF and magnetic flux20.1 Induced EMF and magnetic fluxDefinition of Magnetic FluxJust like in the case of electric flux, Just like in the case of electric flux, consider a situation where the magnetic consider a situation where the magnetic field is uniform in magnitude and field is uniform in magnitude and direction. Place a loop in the Bdirection. Place a loop in the B--field.field.The flux, The flux, ΦΦ, is defined as the product of , is defined as the product of the field magnitude by the area crossed the field magnitude by the area crossed by the field lines.by the field lines.where is the component of B where is the component of B perpendicular to the loop, perpendicular to the loop, θθis the angle is the angle between B and the normal to the loop.between B and the normal to the loop.Units: TUnits: T··mm22or or WebersWebers((WbWb))cosBA BAθ⊥Φ= =B⊥The value of magnetic flux is proportional to the total number of magnetic field lines passing through the loop.121210/7/200310/7/2003Problem: determining a fluxProblem: determining a fluxA square loop 2.00m on a side is placed in a magnetic field of A square loop 2.00m on a side is placed in a magnetic field of strength 0.300T. If the field makes an angle of 50.0° with the strength 0.300T. If the field makes an angle of 50.0° with the normal to the plane of the loop, determine the magnetic flux normal to the plane of the loop, determine the magnetic flux through the loop. through the loop.131310/7/200310/7/2003A square loop 2.00m on a side is placed in a magnetic field of strength 0.300T. If the field makes an angle of 50.0° with the normal to the plane of the loop, determine the magnetic flux through the loop. Solution:Given:L = 2.00 mB = 0.300 Tθ = 50.0˚Find:Φ=?From what we are given, we use cosBAθΦ=()()220.300 2.00 cos50.00.386TmTm==D141410/7/200310/7/200320.1 Induced EMF and magnetic flux20.1 Induced EMF and magnetic fluxFaraday’s experimentTwo circuits are not connected: Two circuits are not connected: no current?no current?However, However, closing the switchclosing the switchwe see that the compass’ we see that the compass’ needle needle movesmovesand then goes and then goes back to its previous positionback to its