Physics 212 Lecture 16 Motional EMF Conductors moing in field nduced emf!! Physics 212 Lecture 16, Slide 1
Music Who is the Artist? A) Gram Parsons ) Tom Waits C) Elis Costello D) Townes Van Zandt E) John Prine Why? Theme of the week? Guys who sing with Emmylou Harris!! do like these albums.. Giing you a break from Jazz this week
Electromotie Force (EMF): f dl Units of EMF: work = force x distance EMF = force/q x distance = work/q = Closed loop integral, so To get a non-zero EMF, need a force that can push charges around a loop, i.e. where f F q fe Force per unit charge of ANY sort e.g.: E f Physics 212 Lecture 16, Slide 5
The ig dea When a conductor moes through a region containg a magnetic field: Magnetic forces may be exerted on the charge carriers in the conductor: F q L X X X X X X X X X F + - F X X X X X X X X X Creates an -> potential difference across the ends of the bar: V f dl ( ) L L due to This is called MOTONAL EMF: Moe a conductor in a magnetic field in the right way, and you e got a magnetic battery in aboe example 05 Physics 212 Lecture 16, Slide 8
Putting it together Change Area of loop Change magnetic field through loop Change orientation of loop relatie to Faraday s Law A d dt We will study this law in detail & in another context next time! Physics 212 Lecture 16, Slide 9
Two identical conducting bars (shown in end iew) are moing through a ertical magnetic field. ar (a) is moing ertically and bar (b) is moing horizontally. Checkpoint 1 Which of the following is true? A. A A motional emf exists in the bar for case (a), but not (b). A motional emf exists in the bar for case (b), but not (a) C C. D A motional emf exists in the bar for both cases (a) and (b) D. A motional emf exists in the bar for neither case (a) nor case (b) :22 Rotate picture by 90 o (top iew) X X X X X X X X X X a + - b F X X X X X X X X X F a = 0 + - F F b = q ar a No magnetic force on charges No charge separation No emf ar b Magnetic force on charges Charge separation emf = (F/q)L = L Physics 212 Lecture 16, Slide 10
A conducting bar (green) rests on two frictionless wires connected by a resistor as shown. Checkpoint 2a Changing Area A The C entire apparatus is placed in a uniform magnetic field pointing into D the screen, and the bar is gien an initial elocity to the right. The motion Rotate of the picture green bar by creates 90 o a current through the bar A. going up A. going down :22 Physics 212 Lecture 16, Slide 11
A conducting bar (green) rests on two frictionless wires connected by a resistor as shown. Checkpoint 2a Equialent circuit Changing Area A The C entire apparatus is placed in a uniform magnetic field pointing into D the screen, and the bar is gien an initial elocity to the right. R V The motion Rotate of the picture green bar by creates 90 o a current through the bar A. going up A. going down X X X X X X X X X F + - F X X X X X X X X X 0 ar Opposite forces on charges Charge separation emf = (F/q)L = 0 L :22 F b = q 0 Physics 212 Lecture 16, Slide 12
A conducting bar (green) rests on two frictionless wires connected by a resistor as shown. F Checkpoint 2b Changing Area A The entire apparatus is placed in a uniform magnetic field pointing into C D the screen, and the bar is gien an initial elocity to the right. The current through this bar results in a force on the bar A. A down. up C. C right D D. E left E. into the screen Preflight 5 Energy External agent must exert force F to the right to maintain constant 0 This energy is dissipated in the resistor! :22 F Counterclockwise Current F L L L R P F points to left F L R L 2 R Physics 212 Lecture 16, Slide 13
A wire loop traels to the right at a constant elocity. Which plot best represents the induced current in the loop as it traels from left of the region of magnetic field, through the magnetic field, and then entirely out on the right side? = 0 = 5 T Out of Screen 20 Checkpoint 5 Physics 212 Lecture 16, Slide 14
A wire loop traels to the right at a constant elocity. Which plot best represents the induced current in the loop as it traels from left of the region of magnetic field, through the magnetic field, and then entirely out on the right side? = 0 = 5 T Out of Screen Let s step through this one 20 Checkpoint 5 Physics 212 Lecture 16, Slide 15
A wire loop traels to the right at a constant elocity. Which plot best represents the induced current in the loop as it traels from left of the region of magnetic field, through the magnetic field, and then entirely out on the right side? L f - + t Only leading side has charge separation emf = L (cw current) A wire loop traels to the right at a constant elocity. Which plot best represents the induced current in the loop as it traels from left of the region of magnetic field, through the magnetic field, and then entirely out on the right side? - L + f f - + t Leading and trailing sides hae charge separation emf = L L = 0 (no current) A wire loop traels to the right at a constant elocity. Which plot best represents the induced current in the loop as it traels from left of the region of magnetic field, through the magnetic field, and then entirely out on the right side? - L f + t 20 Only trailing side has charge separation emf = L (ccw current) Physics 212 Lecture 16, Slide 16
A wire loop traels to the right at a constant elocity. Which plot best represents the induced current in the loop as it traels from left of the region of magnetic field, through the magnetic field, and then entirely out on the right side? = 0 = 5 T Out of Screen 20 Checkpoint 5 Physics 212 Lecture 16, Slide 17
Changing field A conducting rectangular loop moes with elocity toward an infinite straight wire carrying current as shown. Checkpoint 3 What is the direction of the induced current in the loop? A. clockwise. counter-clockwise C. there is no induced current in the loop 20 Physics 212 Lecture 16, Slide 18
Changing field A conducting rectangular loop moes with elocity toward an infinite straight wire carrying current as shown. Checkpoint 3 What is the direction of the induced current in the loop? A. clockwise. counter-clockwise C. there is no induced current in the loop + - + - 20 Physics 212 Lecture 16, Slide 19
Generator: Changing Orientation On which legs of the loop is charge separated? A) Top and ottom legs only ) Front and ack legs only C) All legs D) None of the legs parallel to top and bottom legs Perpendicular to front and back legs 22 Physics 212 Lecture 16, Slide 20
Generator: Changing Orientation L w (A) q = 0 () q = 45 o (C) q = 90 o (D) emf is same at all angles At what angle q is emf the largest? Largest for q = 0 ( perp to ) F w 2EL 2 L 2L 2L( ) cosq Acos( t) q 2 22 = Physics 212 Lecture 16, Slide 21
Generator: Changing Orientation A rectangular loop rotates in a region containing a constant magnetic field as shown. The side iew of the loop is shown at a particular time during the rotation. At this time, what is the direction of the induced (positie) current in segment ab? A. from b to a. from a to b C. there is no induced current in the loop at this time Checkpoint 4 20 Physics 212 Lecture 16, Slide 22
Generator: Changing Orientation A rectangular loop rotates in a region containing a constant magnetic field as shown. The side iew of the loop is shown at a particular time during the rotation. At this time, what is the direction of the induced (positie) current in segment ab? A. from b to a. from a to b C. there is no induced current in the loop at this time + - X Checkpoint 4 20 Physics 212 Lecture 16, Slide 23
Example Problem A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moing away from a long straight wire carrying total current 8 amps. What is the induced current in the loop when it is a distance x=0.7 m from the wire? h x L Conceptual Analysis: Long straight current creates magnetic field in region of the loop. Vertical sides deelop emf due to motion through field Net emf produces current Strategic Analysis: Calculate field due to wire. Calculate motional emf for each segment Use net emf and Ohm s law to get current Physics 212 Lecture 16, Slide 24
Example Problem A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moing away from a long straight wire carrying total current 8 amps. What is the induced current in the loop when it is a distance x=0.7 m from the wire? h x L What is the direction of the field produced by the wire in the region of the loop? A) nto the page ) Out of the page C) Left D) Right E) Up Physics 212 Lecture 16, Slide 25
Example Problem A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moing away from a long straight wire carrying total current 8 amps. What is the induced current in the loop when it is a distance x=0.7 m from the wire? h into page What is the emf induced on the left segment? A) Top is positie ) Top is negatie C) Zero x L Physics 212 Lecture 16, Slide 26
Example Problem A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moing away from a long straight wire carrying total current 8 amps. What is the induced current in the loop when it is a distance x=0.7 m from the wire? h into page x L What is the emf induced on the top segment? A) left is positie ) left is negatie C) Zero perpendicular to wire Physics 212 Lecture 16, Slide 27
Example Problem A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moing away from a long straight wire carrying total current 8 amps. What is the induced current in the loop when it is a distance x=0.7 m from the wire? h into page What is the emf induced on the right segment? A) top is positie ) top is negatie C) Zero x L Physics 212 Lecture 16, Slide 28
Example Problem A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moing away from a long straight wire carrying total current 8 amps. What is the induced current in the loop when it is a distance x=0.7 m from the wire? h into page x L Which expression represents the emf induced in the left wire (A) () left left o 2x o 2x L h q qe o 2x E o 2x h Eh h (C) left o 2 ( L x) L Physics 212 Lecture 16, Slide 29
Example Problem A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moing away from a long straight wire carrying total current 8 amps. What is the induced current in the loop when it is a distance x=0.7 m from the wire? h into page x L Which expression represents the emf induced in the right wire (A) () right right o 2 ( L o h 2x x) h q qe o 2 ( L x) E o 2 ( L Eh h x) h (C) right o 2 ( h x) L Physics 212 Lecture 16, Slide 30
Example Problem A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moing away from a long straight wire carrying total current 8 amps. What is the induced current in the loop when it is a distance x=0.7 m from the wire? h into page x L Which expression represents the total emf in the loop? (A) loop o h o 2x 2 ( L x) h loop loop R () (C) loop loop o h o 2x 2 ( L 0 x) h o loop 2R h 1 x 1 L x Physics 212 Lecture 16, Slide 31
Follow-Up A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moing away from a long straight wire carrying total current 8 amps. What is the direction of the induced current? h x into page + + - - L (A) Clockwise Left > Right () Counterclockwise Clockwise current Physics 212 Lecture 16, Slide 32
Follow-Up A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moing away from a long straight wire carrying total current 8 amps. into page h What is the direction of the force exerted by the magnetic field on the loop? x L (A) () (C) UP DOWN LEFT into page () RGHT () F = 0 Total force from Points to the left!! Physics 212 Lecture 16, Slide 33