# Chapter 20.1 Induced EMF and magnetic flux

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1 Chapter 20.1 nduced EMF and magnetic flux Electric current gives rise to magnetic fields Can a magnetic field give rise to a current? Michael Faraday The answer is yes as discovered by Michael Faraday.

2 Chapter 20.1 nduced EMF and magnetic flux Moving magnetic fields induce currents Change the strength of : nduced current v Moving current loop induces currents nduced EMF!

3 Chapter 20.1 nduced EMF and magnetic flux S units: weber (Wb) Fig. 20.2

4 20.2&20.4 Faraday s law of induction Faraday s law: The induced emf, ɛ, in a closed wire is equal to the time rate of change of the magnetic flux, Φ. An induced emf, ɛ, always gives rise to a current whose magnetic field opposes the original change in magnetic flux. Lenz s law Michael Faraday Faraday s Law and Lenz s Law both state that a loop of wire will want its magnetic flux to remain constant.

5 2. A circular loop with a radius of 0.20 m is placed in a uniform magnetic field =0.85 T. The normal to the loop makes an angle of 30 o with the direction of. The field increases to 0.95 T what is the change in the magnetic flux through the loop? Change in flux? 30 o =0.85T =0.95T Φ = A ' 'cos θ ' Acosθ A' = A = πr θ' Φ = 1.1x10 = θ = 30 o Φ = A = R 2 2 cos θ( ' ) π cos30( ' ) Φ = π 2 (0.2) cos30( ) 2 Wb

6 8. A circular coil with a radius of 20 cm is in a field of 0.2 T with the plane of the coil perpendicular to the field. f the coil is pulled out of the field in 0.30 s find the average emf during this interval Φ Acosθ 0 ε = N = N N= 1 cosθ= A= 1 πr 2 =0 πr ε = = ε = 8.4x π(0.2) 0.3 V

7 20.3 Motional emf A voltage is produced by a conductor moving in a magnetic field V F v L into the page Charges in the conductor experience a force upward F = qv The work done in moving a charge from bottom to top W = FL = qvl The potential difference is W V = = vl q

8 20.3 Motional emf A voltage is produced by a conductor moving in a magnetic field V F v L into the page Charges in the conductor experience a force upward V o lt a g e F = velocity qv W = FL = qvl The potential difference is W V = = vl q

9 20.3 Motional emf The potential difference can drive a current through a circuit The emf arises from changing flux due to changing area according to Faraday s Law wire x A Φ V vl L = = = = = ε R V F v L ε = = R Lv R Changing Magnetic Flux into the page

10 R 18. R= 6.0 Ω and L=1.2 m and =2.5 T. a) What speed should the bar be moving to generate a current of 0.50A in the resistor? b) How much power is dissipated in R? c) Where does the power come from? wire F v a) v v ε Lv = = R R R 0.5(6.0) = = L 2.5(1.2) = 1.0 m/ s V L into the page b) 2 2 P P = R = = 1.5W (0.5) (6.0) c) Work is done by the force moving the bar

11 20.4 Lenz s law revisited Lenz s Law The polarity of the induced emf is such that it induces a current whose magnetic field opposes the change in magnetic flux through the loop. i.e. the current flows to maintain the original flux through the loop. S N V in in acts to oppose the increasing in loop ε - change in flux + Current direction that produces in is as shown (right hand rule) Emf has the polarity shown. ε drives current in external circuit.

12 20.4 Lenz s law revisited Now reverse the motion of the magnet The current reverses direction decreasing in loop S N V ε in + - in acts to oppose the change in flux Current direction that produces in is as shown (right hand rule) Emf has the polarity shown.

13 20.4 Lenz s law revisited Lenz s Law and Reaction Forces S F cm N V N F mc in S A force is exerted by the magnet on loop to produce the current A force must be exerted by the current on the magnet to oppose the change The current flowing in the direction shown induces a magnetic dipole in the current loop that creates a force in the opposite direction

14 20.5 Generators Flux through a rotating loop in a field Normal to the plane θ The flux through the loop ε Φ = Acosθ θ = ωt ω = angular velocity (radians/s)

15 20.5 Generators Φ Relation between Φ and Φ Φ A -A Aω -Aω t t Φ = Acosωt Φ = A ω sinω t proportional to ω

16 20.5 Generators The emf generated by a loop of N turns rotating at constant angular velocity ω is Φ ε = N t ε = NAωsinωt NAω ε 0 -NAω t

17 35. n a model ac generator, a 500 turn rectangular coil 8.0 cmx 20 cm rotates at 120 rev/min in a uniform magnetic field of 0.60 T. a) What is the maximum emf induced in the coil? ε = NAωsinωt The maximum value of ε 20.5 Generators ε ε max max = NAω (120x2 π ) = (500)(0.6)(0.08x0.2) = 60V 60

18 20.5 Generators Alternating Current (AC) generator Rotational Work

19 20.5 Generators Direct Current (DC) generator

20 20.5 Generators A generator is motor acting in reverse ε drives rotation DC motor

21 20.6 Self-nductance a property of a circuit carrying a current a voltage is induced that opposes the change in current used to make devices called inductors Self- inductance of a circuit a reverse emf is produce by the changing current Φ ε = t

22 Self-inductance of a coil ε Self-nductance increases, Current increasing ε changes magnetic flux in the coil, Φ A = Produces emf in coil = = N Φ N A The direction of the induced emf opposes the change in current.

23 A changing current in a coil induces an emf that opposes the change Self-nductance ε - + ε increasing induced emf opposes decreasing induced emf supports

24 20.6 Self-nductance nductance L is a measure of the self-induced emf The self-induced emf is ε Φ ε = N t Current increasing Φ but proportionality constant is L ε = L L is a property of the coil, Units of L, Henry (H) Vs A

25 nductance of a solenoid with N turns and length l, wound around an air core (assume the length is much larger than the diameter). l 20.6 Self-nductance A N Φ = A = µ o A l Φ N = µ o A l ε = Φ = µ = l L 2 N N o A L N = µ o l inductance proportional to N squared x area/length 2 A

26 An air wound solenoid of 100 turns has a length of 10 cm and a diameter of 1 cm. Find the inductance of the coil. l= 10 cm 20.6 Self-nductance d=1 cm L = N N d µ o A = µ π o l l (100) (0.01) = = (4) π 7 2 π 2 5 L x H

27 20.7 RL circuits The inductor prevents the rapid buildup of current ε = L ut at long time does not reduce the current, = at t= 0 τ = Applications of nductors: t τ = o(1 e ) L R Reduce rapid changes of current in circuits Produce high voltages in automobile ignition.

28 20.8 Energy stored in a magnetic field Energy is stored in a magnetic field of an inductor. =0 increasing o ε = o Work is done against ε to produce the field. This produces a change in the PE of the inductor PEL = 1 2 L This stored PE can be used to do work 2

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