# 3/27/2006USF Physics 101 Lecture whatever 1 Physics 101 Spring 2010 Lecture “whatever” Electromagnetic Induction.

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3/27/2006USF Physics 101 Lecture whatever 1 Physics 101 Spring 2010 Lecture “whatever” Electromagnetic Induction

3/27/2006USF Physics 101 Lecture whatever 2 Agenda Proffesor Benton is ill –Terrence A. Mulera HR 102 X5701 mulera @usfca.edu Hours: catch me when you can Faraday’s Law of Electromagnetic Induction –Examples Counter EMFs and Counter Torques Eddy currents General form of Faraday’s Law Inductance

3/27/2006USF Physics 101 Lecture whatever 3 http://terryspeaks.wiki.usfca.edu/ No lab this week

3/27/2006USF Physics 101 Lecture whatever 4  3 ways to generate an induced EMF 1)Change B 2)Change A 3)Change the orientation of B and A

3/27/2006USF Physics 101 Lecture whatever 5 Example: Pulling a 100 loop coil from a magnetic field in t = 0.100 sec Lenz’s law says EMF must be such that it acts to maintain the flux.

3/27/2006USF Physics 101 Lecture whatever 6 If the 100 turn coil has a resistance of 100  Lenz’s law  current circulates clockwise Energy dissipated Force exerted to pull coil out of field can be calculated 2 ways (1) Directly: (2) Energy considerations:

3/27/2006USF Physics 101 Lecture whatever 7 Energy dissipated E = work W needed to pull coil out of field Example: Double the linear dimensions of coil by stretching, don’t move it. Same time interval Stretch the coil Note sign difference. Is this consistent with Lenz’s law?

3/27/2006USF Physics 101 Lecture whatever 8 Example: AC generator

3/27/2006USF Physics 101 Lecture whatever 9 Example: Betatron Changing magnetic field

3/27/2006USF Physics 101 Lecture whatever 10

3/27/2006USF Physics 101 Lecture whatever 11 Donald Kerst University of Illinois

3/27/2006USF Physics 101 Lecture whatever 12 Counter EMF: Electric motor turns and produces mechanical energy when current runs through it. As motor turns induction produces a counter EMF which acts to oppose the motion. Counter EMF  speed Motor reaches some equilibrium speed Add mechanical load, motor is slowed, counter EMF is reduced and current flows. A stalled electric motor can draw large current and burn out

3/27/2006USF Physics 101 Lecture whatever 13 Counter torque: Turning produces an EMF. If generator is not connected to anything we get an EMF but no current flows. G G Load Add current drawing load. Current flows in generator coils and magnetic field exerts a torque which opposes the rotation. The greater the load, the greater the counter torque.

3/27/2006USF Physics 101 Lecture whatever 14 Eddy currents: Induced currents in bulk material Rotating metal wheel Point c, B = 0 → B in Induced current is counterclockwise to oppose change Point e, B in → B = 0. Induced current is clockwise. Magnetic force acts to oppose rotation of the wheel.

3/27/2006USF Physics 101 Lecture whatever 15 Eddy currents can be useful for braking or oscillation damping but also waste energy throgh I 2 R heating in the iron cores of motors, generators and transformers. Thin sheets of Fe insulated from one another

3/27/2006USF Physics 101 Lecture whatever 16 Transformers revisited: Kirchoff loop rule  Assuming no flux is lost Conservation of energy  output power = input power

3/27/2006USF Physics 101 Lecture whatever 17 General form of Faraday’s Law: Changing magnetic flux induces a current in a wire   An electric field doing the work to move charges in the wire A changing magnetic field produces an electric field The emf induced in a circuit is the work done by E to move a unit charge around the circuit

3/27/2006USF Physics 101 Lecture whatever 18 Maxwell’s Equations (integral form)

3/27/2006USF Physics 101 Lecture whatever 19 Example: Magnetic field between pole faces of a magnet Valid for r r 0

3/27/2006USF Physics 101 Lecture whatever 20 Note that the more general form of Faraday’s Law is valid not only in conductors but in any region of space,

3/27/2006USF Physics 101 Lecture whatever 21 Inductance Mutual Inductance: M 21 depends only on the geometry and contents of the 2 coils (like capacitance) Now reverse the situation:

3/27/2006USF Physics 101 Lecture whatever 22 Units of M are henries (H) Self Inductance: Changing current in a coil → changing flux through coil → opposing EMF. All circuits have some (self) inductance

3/27/2006USF Physics 101 Lecture whatever 23 Example: Apply Lenz’s Law (a) I is increasing so  is  Induced EMF acts to retard I (b) I is decreasing so  is (-) Induced EMF acts to assist I Example: Inductance of a solenoid, N = 100, l = 5.0 cm and A = 0.30 cm 2 For an air filled coil

3/27/2006USF Physics 101 Lecture whatever 24 Now, add an Fe core with  = 4000  0 to the solenoid L will be 4000 x larger or L = 30 mH

3/27/2006USF Physics 101 Lecture whatever 25 Networking rules for inductances: The above neglects mutual inductance

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