Conductors moving in B field Physics 212 Lecture 16 Motional EMF Induced emf !! Conductors moving in B field

Music Who is the Artist? Gram Parsons Tom Waits Elvis Costello Townes Van Zandt John Prine Why? Theme of the week? Guys who sing with Emmylou Harris !! I do like these albums.. Giving you a break from Jazz this week… Physics 212 Lecture 3

Electromotive Force (EMF): Force per unit charge of ANY sort e.g.: where Units of EMF: work = force x distance EMF = force/q x distance = work/q = VOLTS Closed loop integral, so … To get a non-zero EMF, need a force that can push charges around a loop, i.e. drive a circuit

The Big Idea B When a conductor moves through a region containg a magnetic field: Magnetic forces may be exerted on the charge carriers in the conductor: Creates an EMF -> potential difference across the ends of the bar: X X X X X X X X X + - F L v X X X X X X X X X in above example This is called MOTIONAL EMF: Move a conductor in a magnetic field in the right way, and you’ve got a magnetic battery 05

Putting it together Faraday’s Law Change Area of loop Change magnetic field through loop Change orientation of loop relative to B 2nd way to calculate motional EMF Faraday’s Law We will study this law in detail & in another context next time !

No magnetic force on charges Magnetic force on charges Two identical conducting bars (shown in end view) are moving through a vertical magnetic field. Bar (a) is moving vertically and bar (b) is moving horizontally. Checkpoint 1 B Which of the following is true? A. A motional emf exists in the bar for case (a), but not (b) B. A motional emf exists in the bar for case (b), but not (a) C. 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) A B C D Rotate picture by 90o (top view) v X X X X X X X X X B X b a Bar a No magnetic force on charges No charge separation No emf + - F Fb = qvB + - v || B  Fa = 0 Bar b Magnetic force on charges Charge separation emf = (F/q)L = vBL :22

Changing Area Rotate picture by 90o A conducting bar (green) rests on two frictionless wires connected by a resistor as shown. Checkpoint 2a Changing Area A B The entire apparatus is placed in a uniform magnetic field pointing into the screen, and the bar is given an initial velocity to the right. The motion of the green bar creates a current through the bar A. going up B. going down C D Rotate picture by 90o A B :22

Opposite forces on charges A conducting bar (green) rests on two frictionless wires connected by a resistor as shown. Checkpoint 2a V R I Equivalent circuit Changing Area A B The entire apparatus is placed in a uniform magnetic field pointing into the screen, and the bar is given an initial velocity to the right. The motion of the green bar creates a current through the bar A. going up B. going down C D Rotate picture by 90o A B v0 X X X X X X X X X B + - F Fb = qv0B Bar Opposite forces on charges Charge separation emf = (F/q)L = v0BL :22

Counterclockwise Current A conducting bar (green) rests on two frictionless wires connected by a resistor as shown. Checkpoint 2b F points to left F I Energy External agent must exert force F to the right to maintain constant v0 This energy is dissipated in the resistor! Changing Area A The entire apparatus is placed in a uniform magnetic field pointing into the screen, and the bar is given an initial velocity to the right. The current through this bar results in a force on the bar A. down B. up C. right D. left E. into the screen B C D A B Preflight 5 C D E Counterclockwise Current :22

A wire loop travels to the right at a constant velocity A wire loop travels to the right at a constant velocity. Which plot best represents the induced current in the loop as it travels from left of the region of magnetic field, through the magnetic field, and then entirely out on the right side? B = 0 B = 5 T Out of Screen v Checkpoint 5 20

Let’s step through this one A wire loop travels to the right at a constant velocity. Which plot best represents the induced current in the loop as it travels from left of the region of magnetic field, through the magnetic field, and then entirely out on the right side? B = 0 B = 5 T Out of Screen v Let’s step through this one Checkpoint 5 20

- t + t - - + + - t + fB L v Only leading side has charge separation A wire loop travels to the right at a constant velocity. Which plot best represents the induced current in the loop as it travels from left of the region of magnetic field, through the magnetic field, and then entirely out on the right side? + - fB t L v Only leading side has charge separation emf = BLv (cw current) A wire loop travels to the right at a constant velocity. Which plot best represents the induced current in the loop as it travels from left of the region of magnetic field, through the magnetic field, and then entirely out on the right side? v + - fB L t + - fB Leading and trailing sides have charge separation emf = BLv – BLv = 0 (no current) A wire loop travels to the right at a constant velocity. Which plot best represents the induced current in the loop as it travels from left of the region of magnetic field, through the magnetic field, and then entirely out on the right side? v L + - fB t Only trailing side has charge separation emf = BLv (ccw current) 20

A wire loop travels to the right at a constant velocity A wire loop travels to the right at a constant velocity. Which plot best represents the induced current in the loop as it travels from left of the region of magnetic field, through the magnetic field, and then entirely out on the right side? B = 0 B = 5 T Out of Screen v Checkpoint 5 20

Changing B field Checkpoint 3 A conducting rectangular loop moves with velocity v toward an infinite straight wire carrying current as shown. Checkpoint 3 What is the direction of the induced current in the loop? A. clockwise B. counter-clockwise C. there is no induced current in the loop 20

Changing B field Checkpoint 3 + - B  + - v I A conducting rectangular loop moves with velocity v toward an infinite straight wire carrying current as shown. Checkpoint 3 What is the direction of the induced current in the loop? A. clockwise B. counter-clockwise C. there is no induced current in the loop I  B v + - + - 20

Generator: Changing Orientation On which legs of the loop is charge separated? Top and Bottom legs only Front and Back legs only All legs None of the legs Perpendicular to front and back legs parallel to top and bottom legs 22

Generator: Changing Orientation L w At what angle q is emf the largest? Largest for q = 0 (v perp to B) (A) q = 0 (B) q = 45o (C) q = 90o (D) emf is same at all angles = v 22

Generator: Changing Orientation A rectangular loop rotates in a region containing a constant magnetic field as shown. The side view of the loop is shown at a particular time during the rotation. At this time, what is the direction of the induced (positive) current in segment ab? A. from b to a B. from a to b C. there is no induced current in the loop at this time Checkpoint 4 20

Generator: Changing Orientation A rectangular loop rotates in a region containing a constant magnetic field as shown. The side view of the loop is shown at a particular time during the rotation. At this time, what is the direction of the induced (positive) current in segment ab? A. from b to a B. from a to b C. there is no induced current in the loop at this time Checkpoint 4 B v  + - I X 20

Example Problem A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving 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? v I h x L Conceptual Analysis: Long straight current creates magnetic field in region of the loop. Vertical sides develop emf due to motion through B field Net emf produces current Strategic Analysis: Calculate B field due to wire. Calculate motional emf for each segment Use net emf and Ohm’s law to get current

Example Problem A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving 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? v I h x L What is the direction of the B field produced by the wire in the region of the loop? Into the page Out of the page Left Right Up

Example Problem B into page v I h x L A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving 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? B into page v I h x L What is the emf induced on the left segment? Top is positive Top is negative Zero

Example Problem B into page v I h x L perpendicular to wire A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving 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? B into page v I h x L What is the emf induced on the top segment? left is positive left is negative Zero perpendicular to wire

Example Problem B into page v I h x L A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving 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? B into page v I h x L What is the emf induced on the right segment? top is positive top is negative Zero

Example Problem B into page v I h x L A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving 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? B into page v I h x L Which expression represents the emf induced in the left wire (A) (B) (C)

Example Problem B into page v I h x L A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving 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? B into page v I h x L Which expression represents the emf induced in the right wire (A) (B) (C)

Example Problem B into page v I h x L A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving 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? B into page v I h x L Which expression represents the total emf in the loop? (A) (B) (C)

Follow-Up eLeft > eRight B into page + - I Clockwise current v I h A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving away from a long straight wire carrying total current 8 amps. B into page + - eLeft > eRight I Clockwise current v I h x L What is the direction of the induced current? (A) Clockwise (B) Counterclockwise

Follow-Up B into page I v I h A rectangular loop (h=0.3m L=1.2 m) with total resistance of 5W is moving away from a long straight wire carrying total current 8 amps. B into page I v I h What is the direction of the force exerted by the magnetic field on the loop? x L (A) UP I B into page (B) DOWN Total force from B Points to the left !! (C) LEFT (B) RIGHT (B) F = 0