Ch. 22 Electromagnetic Induction

Transcription

1 Ch. 22 Electromagnetic Induction 22.1 Induced emf So electric current (moving charge) create agnetic Field. I the revere true? Can magnetic field create current??? D Ye!!! ut it take a changing magnetic field to produce a current!!! After Oerted dicovery, it took 12 year to move the magnet! Notice: A current would alo be produced if I held the magnet tationary and moved the coil! The field in the coil i till changing! The current that i produced in the coil i called an induced current. The coil then act like a battery, or a ource of emf. Thi emf i called an induced emf. The current and emf (voltage) are called induced, becaue they are due to the changing magnetic field.. Another way to induce an emf and produce a current in the coil i to change the area of the coil: 0 0 Either enlarging the coil or hrinking it will produce an induced current. A long a the area of the loop keep changing, an induced current will flow! So why doe thi happen??? The coil i a conductor, and thu contain charge which can move eaily. 1

2 Since I m moving the conductor which contain charge, I m moving the charge in a magnetic field. Thu they feel a force! The phenomenon of producing induced emf with a changing magnetic field i called Electromagnetic Induction otional emf L What happen if we move a conducting rod at right angle to a uniform magnetic field? When the rod move, the electron in the rod feel a force, ince they are charge + moving in a magnetic field: x - x x x x x x x x x x x x x y RHR-1, the electron move to the bottom of the rod, and poitive charge move to the top. Thu, the rod act a a ource of emf, like a battery. The induced emf i called a motional emf. (motion of charge through a mag. Field) L An electric field i etup within the rod, and the eparation of charge along the rod continue until the attractive electrical force between the charge equal the magnetic force. x x x + x x x x x x x x x x x v E - What i the magnitude of the emf? Once no further charge F = E F E F F = eparation take place. The motional emf i maintained a long a the bar keep moving. If v = 0, then F = qvinθ = 0 and F E will reunite the + and charge, thu eliminating the emf.! = vl ε i the induced emf (voltage) v i the peed of the bar i the magnetic field L i the length of the bar in the field Thi i true when v,, and L are mutually perpendicular. 2

3 22.2 (cont.) otional emf So a motional emf occur when a conductor i moved through a magnetic field. Let form a complete circuit with the conducting rod, o that a current can flow. I Light bulb I xxxxxxxxx + xxxxxxxxx I xxxxxxxxx xxxxxxxxx v xxxxxxxxx xxxxxxxxx I F Conducting rail (frictionle) When we lide the bar to the right at peed v, an induced emf i et up acro the bar, and an induced current will flow. What i the direction of the induced current? The bar act like a battery, o the current flow counter-clockwie. ut now the current in the moving bar feel a force from the magnetic field! y RHR-1 thi force i directed to the left! The force oppoe the direction of motion of the rod. The rod will top, unle a larger force keep pulling it to the right. A the rod lide, the light bulb ue energy. Where doe the energy come from??? It come from the force puhing the rod to the right! We mut have conervation of energy. So the work done on the rod in liding it to the right i equal to the energy conumed by the light bulb! And.ore importantly: When a motional emf lead to an induced current, a magnetic force will act to oppoe the motion in accord with the rinciple of Conervation of Energy. Thi i the foundation for Lenz Law which we will get to in

4 22.3 agnetic Flux In ch. 18 we defined the electric flux through a urface element A a: " E = E# A = EAco! We can do a imilar thing for magnetic field: Normal coφ φ A " =! A = Aco! " = Aco! Thi i the magnetic flux through urface A. Unit? 2 (agnetic Field)!(Area) = [ T! m ] = [ Weber] = [ Wb] So, the magnetic flux will be maximum when the field i perpendicular to the urface! " = Aco! Notice that "! Thu, if increae then the magnetic flux Φ alo increae. Remember that the magnitude of i repreented by the denity of field line. The more field line I have per unit area, the tronger the field. Thu, the more field line I have per unit area, the bigger the flux. "!! (the # of field line thru a urface) A A ore field line thru the ame area greater flux! 4

5 Now let reexamine our liding conducting bar in term of agnetic Flux: L Light bulb xxxxxxxxx + + xxxxxxxxx xxxxxxxxx xxxxxxxxx A v xxxxxxxxx o A f v xxxxxxxxx t = 0 t = t o x o x f t = t f Conducting rail (frictionle) Let the bar tart at t = 0. Now let the bar move to it poition when t = t o. The bar move a ditance x o and weep out an area A o. Now let the bar lide for a longer time to t f. It move to poition x f and weep out an area A f. We know the emf acro the bar i:! x!( xl)!( A)! = vl = L = =!(" ) =!( " A)!(" = = # Thu, the induced emf i equal to the change in the magnetic flux divided by the change in time! ) Thi i uually written a: $ = #!" The minu ign i here, becaue the induced current flow in a direction uch that the magnetic field it create oppoe the change in the magnetic flux Faraday Law of Electromagnetic Induction Often time the magnetic flux will pa thru a coil with multiple turn:!" = # N $ Thi i Faraday Law. N i the # of turn in the coil. Unit? Volt [V] So an emf i induced whenever Φ change in time for any reaon! Since " = Aco!, So, we could write Faraday Law a: That mean that if, A, or φ change in time, then an emf i induced! $ "!( Aco# ) = 5

6 22.5 Lenz Law Remember Faraday Law:!" $ = # N, where " = Aco!. So a changing magnetic field can produce a current. What i the direction of thi current? To get the direction, we mut conider two magnetic field: The firt i the original one that produced the induced current. The econd i the field created by the induced current itelf. To determine the direction of the induced current flow, we ue Lenz Law: The induced emf reulting from a change in magnetic flux lead to an induced current which produce a magnetic field to oppoe the change in flux. Example: Conider a ingle loop of wire itting in the plane of the paper: xxxxxxxxxxx xxxxxxxxxxx Ι xxxxxxxxxxx xxxxxxxxxxx Now turn on a magnetic field everywhere into the page: Then, in all of thee Lenz Law problem, you have to ak yourelf two quetion: Firt, what i the direction of the magnetic flux? In other word, what direction doe the original magnetic field point? Here, it tarted out at ZERO. Second quetion: I the flux increaing or decreaing? Here, it i increaing. So, we have an increaing magnetic flux directed into the page. Lenz Law tell u the induced current will flow in the direction that will create a new magnetic field to oppoe thi change. Thu, if we have an increaing magnetic flux into the page, then we hould create a field pointing out of the page to oppoe thi change. y uing RHR-3, we ee that to create a magnetic field out of the page, my induced current in the loop mut flow ccw! Thi reult in the proper direction for the induced field! 6

7 Now let take the ame loop again and place it in a uniform magnetic field that exit everywhere out of the page: Now decreae the field. Will there be an induced current? Ι Ye, ince we have a change in magnetic flux! 1. What i the direction of the flux? Out of the page 2. I it increaing or decreaing? Decreaing Thu, we have a decreaing magnetic flux that point out of the page. To oppoe thi change, Lenz Law tell u an induced current will flow to create a induced field that trie to maintain the flux out of the page. Thu, by RHR-3, we need a ccw current! If there i initially no flux through the loop, then Lenz Law trie to keep it out. If there i flux initially through the loop, then Lenz Law trie to keep it there. It alway oppoe the change! Another way to remember thi i the following: If the original field i increaing, then the induced field mut point in the oppoite direction. If the original field i decreaing, then the induced field mut point in the ame direction. Now let lide a conducting ring through a region of pace where the magnetic field point into the creen: A the ring lide, let ak ourelve when an induced current would flow, and in what direction. Let analyze 5 different point along the ring path. 1. efore it enter the field. 2. A it enter the field. 3. While it completely in the field. 4. A it leave the field. 5. After it ha left the field. 7

8 I there an induced current in the ring at poition 1? No! No change in flux! I there an induced current in the ring at poition 2? Ye! Change in flux! The flux i increaing into the page. Lenz tell u we need an induced field that point out of the page. y RHR-3, thi i a ccw current. I there an induced current in the ring at poition 3? No! No change in flux! I there an induced current in the ring at poition 4? Ye! Change in flux! The flux i decreaing into the page. Lenz tell u we need an induced field that point into the page. y RHR-3, thi i a cw current. I there an induced current in the ring at poition 5? No! No change in flux! Review - Field and Current A wire carrying a current create a magnetic field LENZ Law A changing magnetic field within a conducting loop create a current that oppoe the change Induced current Faraday Law.!" $ = # N oppoing Increaing A current loop create a magnetic field 8

9 D 22.8 utual and Self Induction Let place two coil ide by ide. Let connect one to an AC generator (primary coil) and the other to a voltmeter (econdary coil): The primary coil create a magnetic field, and ome of thoe field line pa thru the econdary coil. Thi produce a change in magnetic flux in the econdary coil, leading to an induced emf! Thi i called utual Inductance. $ From Faraday Law: #,!" where ε i the induced emf in the econdary coil, and ΔΦ i the change in mag. flux thru the econdary coil. The net flux thru the econdary coil i: Where N i the number of turn in the econdary coil. N!! I Thu, the flux thru the econdary coil i proportional to the current in the primary. ake thi an equality: N! = I " N! = I i a quantity called the utual Inductance. We can ubtitute thi into Faraday Law:!"!( N $ = # N " )!( I = # ) = " = "! I! I # $ = " Now it eay to ee that the induced emf in the econdary coil depend on the changing current in the primary coil. 9

10 Unit? & $ % V ' A #! "! [ Henry ]! [ H] So, inductance come in henrie. 1 H i a pretty big inductance. Often ue mh or µh. Self Inductance Conider jut one coil connected to an AC generator: The AC current produce a changing magnetic field which produce a change in mag. flux within the coil. Thi lead to an induced emf in the coil! Thi proce i called Self Induction. Let Φ be the flux thru one loop of the coil, o NΦ i the net flux. "!! I So, N "! I. ake thi an equality: N! = LI L N! I = L i a quantity called the Self Inductance. Uing Faraday Law again, like we did for mutual inductance, we find:!i # = "L 22.9 Tranformer We can ue one coil to induce an emf (voltage) in another coil by mutual induction. 10

11 The bet part about a tranformer i that the induced emf in the econdary coil i proportional to the turn ratio: N S N N = # of turn in the econdary coil N = # of turn in the primary coil Thu, the more turn I have in the econdary coil, the higher the induced emf! The iron core enure the flux through each coil i the ame, and we get: V = V N N Thi i the tranformer equation. V = Voltage in the econdary coil V = Voltage in the primary coil A tranformer can either increae or decreae the primary voltage: If N > N, then the tranformer i called a tep-up tranformer. If N < N, then the tranformer i called a tep-down tranformer. Example: ug Zapper Thee device plug into a tandard houe outlet at 120 V, and they have a tep-up tranformer inide which convert thi primary voltage into 5000 V. If the primary coil ha 21 turn, how many turn doe the econdary have? From the tranformer equation: V (5000) N = N = ( 21) = 875 turn V (120) ut what happen when I go from 120 V to 5000 V? I can t get omething for nothing! I mut have Conervation of Energy! Energy delivered to the primary coil = Energy delivered to the econdary coil 11

12 Energy i jut ower x Time, o the power in each coil mut be equal: I V = I S V S V! I S = I Thu, if I have a tep-up tranformer, V then V S > V, and the current in the S econdary (I S ) goe down! Thi aume no lo due to heat in the tranformer, which for good one, i about 1%. 12