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<ul><li> 1. Faradays Law Physics 102:Lecture 10 Changing Magnetic Fields create Electric Fields</li></ul> <p> 2. Last Two Lectures </p> <ul><li>Magnetic fields </li></ul> <ul><li>Forces on moving charges and currents </li></ul> <ul><li>Torques on current loops </li></ul> <ul><li>Magnetic field due to </li></ul> <ul><li><ul><li>Long straight wire </li></ul></li></ul> <ul><li><ul><li>Solenoid </li></ul></li></ul> <p> 3. Motional EMF </p> <ul><li>A metal bar slides with velocity v on a track in a uniform B field</li></ul> <ul><li>Moving + charges in bar experience force down (RHR1) </li></ul> <ul><li>Electrical current driven clockwise! </li></ul> <ul><li>Moving baracts like a battery(i.e. generates EMF)!! </li></ul> <p>(Recall that e- actually move, opposite current) V F q + q I 4. Faradays Law of Induction: </p> <ul><li> induced EMF = rate of change of magnetic flux </li></ul> <ul><li>The principle that unifies electricity and magnetism </li></ul> <ul><li>Key to many things in E&amp;M </li></ul> <ul><li><ul><li>Generating electricity </li></ul></li></ul> <ul><li><ul><li>Microphones, speakers, guitar pickups </li></ul></li></ul> <ul><li><ul><li>Amplifiers </li></ul></li></ul> <ul><li><ul><li>Computer disks and card readers </li></ul></li></ul> <p> 5. First a preliminary:Magnetic Flux </p> <ul><li> Counts number of field lines through loop. </li></ul> <p>Uniform magnetic field,B , passes through a plane surface of areaA . Magnetic flux = B A (Units Tm 2= Wb) Magnetic flux B Acos( ) is angle betweennormalandB B A B A normal Note: The flux can be negative (if field lines go thru loop in opposite direction) 6. Preflight 10.7 </p> <ul><li>Compare the flux through loops a and b. </li></ul> <ul><li>1) a &gt; b 2) a &lt; b </li></ul> <p>a b n n B A= B A cos(0) = BA B= B A cos(90) = 0 more lines pass through its surface in that position. 7. Faradays Law of Induction: </p> <ul><li> induced EMF = rate of change of magnetic flux </li></ul> <ul><li>Since = B A cos( ), 3 things can change </li></ul> <ul><li><ul><li><ul><li>Area of loop </li></ul></li></ul></li></ul> <ul><li><ul><li><ul><li>Magnetic field B </li></ul></li></ul></li></ul> <ul><li><ul><li><ul><li>Anglebetween normal and B </li></ul></li></ul></li></ul> <p> 8. ACT: Change Area1 v v 3 Which loop has the greatest induced EMF at the instant shown above? L W 2 v 9. Faraday: Change AreaV t=0 0 =BLW t t =BL(W+vt) L W EMF Magnitude: = B A cos( ) Example What about thesignof the EMF? V W vt 10. Lenzs Law (EMF direction) V </p> <ul><li>Flux is increasing </li></ul> <ul><li>Induced current is clockwise </li></ul> <ul><li>Current loop generatesinduced B field </li></ul> <ul><li><ul><li>from RHR2, into page, opposite external B field! </li></ul></li></ul> <p>What happens if the velocity isreversed ? V I B ind 11. Lenzs Law (EMF direction) V </p> <ul><li>Flux is decreasing </li></ul> <ul><li>Induced current iscounterclockwise </li></ul> <ul><li>Current loop generates induced B field</li></ul> <ul><li><ul><li>from RHR2,out of the page , along external B field! </li></ul></li></ul> <p>Induced EMFopposes changein fluxV I B ind 12. Lenzs Law(EMF Direction) Induced emfopposes changein fluxEMF does NOT oppose B field, or flux! EMF opposes theCHANGEin flux </p> <ul><li>If flux increases:</li></ul> <ul><li>New EMF makes new fieldopposite tooriginal field </li></ul> <ul><li>If flux decreases: </li></ul> <ul><li><ul><li>New EMF makes new fieldin same direction asoriginal field </li></ul></li></ul> <p> 13. Motional EMF circuit </p> <ul><li>Direction of Current </li></ul> <ul><li>B field generates force on current-carrying bar </li></ul> <p>I = /R </p> <ul><li>Magnitude of current </li></ul> <p>Clockwise ( +charges godownthru bar,upthru bulb) F bar= ILB sin( ), t o left (RHR1) V F baropposes v! = vBL/R </p> <ul><li>Careful! There are two forces: </li></ul> <p>F bar= force on bar from induced current F q= force on + charges in bardrivinginduced current I F q + q F bar 14. Motional EMF circuit </p> <ul><li>Direction of Current </li></ul> <p>xxx xxxx xxxx xxxx xxxxx xxxx xxxx xxxx xxxxx xxxx xxxx xxxx xxxxx xxxx xxxx xxxx xxxxx xxxx xxxx xxxx xxI = /R= vBL/R Still to left, opposite v What happens if field isreversed ? (TRY IT AT HOME) V </p> <ul><li>Direction of force(F=ILB sin( ))on bar due to magnetic field </li></ul> <ul><li>Magnitude of current </li></ul> <p>Counter-Clockwise ( +charges goupthru bar,downthru bulb) F always opposes v, bar slows down Must apply external force to keep bar moving 15. Preflight 10.4 </p> <ul><li>Increase </li></ul> <ul><li>Stay the Same </li></ul> <ul><li>Decrease </li></ul> <p>To keep the bar moving at the same speed, the force supplied by the hand will have to: F=ILB sin( ) 16. Preflight 10.5 </p> <ul><li>True </li></ul> <ul><li>False </li></ul> <p>To keep the bar moving to the right, the hand will have to supply a force in the opposite direction. 17. Faradays Law of Induction: </p> <ul><li> induced EMF = rate of change of magnetic flux </li></ul> <ul><li>Since = B A cos( ), 3 things can change </li></ul> <ul><li><ul><li><ul><li>Area of loop </li></ul></li></ul></li></ul> <ul><li><ul><li><ul><li>Magnetic field B </li></ul></li></ul></li></ul> <ul><li><ul><li><ul><li>Anglebetween normal and B </li></ul></li></ul></li></ul> <p> 18. ACT: Induction cannon (Demo) </p> <ul><li>As current increases in the solenoid, what direction will induced current be in ring? </li></ul> <ul><li>Same as solenoid </li></ul> <ul><li>Opposite of solenoid </li></ul> <ul><li>No current </li></ul> <p>A solenoid is driven by an increasing current. A loop of wire is placed around it B sol 19. Induction cannon (Demo) </p> <ul><li>Recall: current loop behaves like bar magnet </li></ul> <ul><li>Opposite currents =&gt; opposite polarities </li></ul> <ul><li>Like poles repel! Loop shoots up </li></ul> <p>A solenoid is driven by an increasing current. A loop of wire is placed around it </p> <ul><li>What happens when loop has less resistance? </li></ul> <ul><li>What happens if the loop is broken? </li></ul> <p> 20. </p> <ul><li>Which way is the magnet moving if it is inducing a current in the loop as shown? </li></ul> <ul><li>Up </li></ul> <ul><li>Down </li></ul> <p>ACT: Change B (Demo) Demo 371 21. ACT: Change B II (contd) </p> <ul><li>If I reduce the resistance in the wire, the magnet will fall</li></ul> <ul><li>faster </li></ul> <ul><li>slower </li></ul> <ul><li>at the same speed </li></ul> <p>N S 22. Magnetic Flux Examples A conducting loop is inside a solenoid (B= o nI).What happens to the flux through the loop when you Increase area of solenoid? Increase area of loop? Increase current in solenoid? Rotate loop slightly? Nothing Increases B Acos( ) Increases Decreases Example 23. Magnetic Flux II Increase area of solenoid Increase area of loop Increase current in solenoid Increases Nothing Increases A solenoid (B= o nI) is inside a conducting loop.What happens to the flux through the loop when you B Acos( ) Example 24. Faradays and Lenzs Law </p> <ul><li>Faraday: Induced emf = rate of change of magnetic flux </li></ul> <ul><li>Since = B A cos( ), 3 things can change </li></ul> <ul><li><ul><li><ul><li>Area of loop </li></ul></li></ul></li></ul> <ul><li><ul><li><ul><li>Magnetic field B </li></ul></li></ul></li></ul> <ul><li><ul><li><ul><li>Anglebetween normal and B </li></ul></li></ul></li></ul> <p> Next lecture Lenz: Induced emfopposes changein flux </p>