FARADAY S LAW ELECTROMAGNETIC INDUCTION

Transcription

1 FARADAY S LAW ELECTROMAGNETIC INDUCTION magnetic flux density, magnetic field strength, -field, magnetic induction [tesla T] magnetic flux [weber Wb or T.m 2 ] A area [m 2 ] battery back t T f angle between magnetic field and direction perpendicular to area element [degrees] induced emf [V] emf of a battery [V] induced emf in the coils of a rotating motor that opposes the rotation [V] time interval [s] period of rotation [s] frequency of rotation [hertz Hz] angular frequency [rad.s - ] I current through coils of motor [ampere A] R resistance of motor coils [ohms ] Magnetic flux Magnetic flux for constant -field Acos Each point on a surface is associated with a direction, called the surface normal; the magnetic flux through a point is then the component of the magnetic field along this direction A 90 o cos A Acos 0 o cos 0 0 Equation Mindmap eq4: Doing Physics on Line

2 Faraday s Law t d dt A changing magnetic field induces a changing electric field. A changing magnetic flux induces a changing electric field The changing electric field induces an emf in a conductor. In a conductor loop, the changing emf induces a current. The above processes are known as electromagnetic induction. Lenz s law the induced emf and induced current are in such a direction as to oppose the change that produces them. Equation Mindmap eq4: Doing Physics on Line 2

3 Equation Mindmap eq4: Doing Physics on Line 3

4 F force on electron right hand palm rule fingers thumb I palm F v velocity of electron in conductor uniform -field out of page I uniform -field out of page right hand palm rule fingers thumb I palm F R motion of conductor Direction of induced force on conductor by the current flowing in the circuit. The direction of the induced force opposes the motion of the conductor through the -field. induced magnetic field into page produced by the clockwise induced current Equation Mindmap eq4: Doing Physics on Line 4

5 GENERATORS Acos t t Asin t AC generator magnetic field in +x direction D n N C E S direction of rotation clockwise around z axis (out of page) slip rings F brush contacts A to external circuit z y x Each end of the rotating loop is attached to a metal hoop called a slip ring. The slip rings turn with the loop, but as they turn they rub against two electrical brush contacts. The brushes are fixed and carry the current produced in the rotating loop into the external circuit. This arrangement ensures that the direction of the current supplied to the external circuit will also be reversed for each half of a revolution. Generator parameters: number of winding of coil N rotation speed [rad.s - ] rotation frequency f = / 2 [Hz] period of rotation T = /f = 2/ [s] angle between magnetic field and normal to the area of the coil t [rad] magnetic flux (constant magnetic field) Acos( ) Acos( t) [T.m 2 ] d emf N N Asin( t) N 2 f Asin(2 f t) dt induced emf Equation Mindmap eq4: Doing Physics on Line 5

6 Example A rectangular coil of length 35 mm and width 25 mm is rotated at a constant rate of 500 Hz in a uniform magnetic field of strength T. Graph the change in magnetic flux and induced emf as functions of time. If the resistance of the coil and external circuit connected to the generator is 650 ma, what is the maximum current in the external circuit? Solution L = 35x0-3 m L 2 = 25x0-3 m A = L L 2 = x0-4 m 2 f = 500 Hz T = / f = 2x0-3 s 2 f = 3.46x0 3 rad.s - = T N = 500 turns A= 4.4x0-5 Wb max dcos t N A N Asin t dt max N A = 69 V Approximation of max max max 0 = 44 V t T /4 Equation Mindmap eq4: Doing Physics on Line 6

7 N d dt negative slope of vs t graph max slope = 0 T/4 max neg slope max pos slope Equation Mindmap eq4: Doing Physics on Line 7

8 A (0,0) _ 3 4 time t A slip ring A2 3 4 (0,0) _ load brushes ac voltage across load time t rotation of axle (hand or petrol motor etc) slip rings coil windings attached to the slip rings and turned by the rotation of the axle brushes for connections to external circuit: brushes remain stationary as commutator rotates rushes are used to make the connections between the generator and external circuit. For a ac generator a pair of slip rings are used. DC generator rushes are used to make the connections between the generator and external circuit. For a DC generator a single split ring commutator. is used. Equation Mindmap eq4: Doing Physics on Line 8

9 ELECTRIC MOTOR and back emf IR supply battery back battery motor supply R coil back V coil Example The armature windings of a DC motor has a resistance of 5.0. The motor is connected to a 240 V power supply. When the motor reaches its full rotation speed the back emf is 88 V. (a) When the motor is just starting, what the motor current? (b) What is the current when the motor is operating at its maximum rotation speed? Solution R = 5.0 = 240 V back = 88 V Motor starting I I coil coil V R coil coil As coil rotates in the magnetic field, an emf is induced in the coil (back emf) to oppose its motion. supply R coil back back = 0 V I =? A I = / R = (240 / 5) A = 48 A Motor max speed back = 88 V I =? A I = ( - back ) / R = (240-88) / 5 A = 0 A Faster the rotation speed the greater the induced back emf. Currents can be very high on starting. When a motor is jammed rotation speed much reduced reduced emf increased current motor heats up motor maybe damaged. Equation Mindmap eq4: Doing Physics on Line 9