Physics 212 Lecture 16 Motional EMF Conductors moving

Physics 212 Lecture 16 Motional EMF Conductors moving in B field Induced emf !! Physics 212 Lecture 16, Slide 1

The Big Idea When a conductor moves through a region containg a magnetic field: § Magnetic forces may be exerted on the charge carriers in the conductor B XXXXX F L + - v F XXXXX § § 05 These forces produce a charge separation in the conductor This charge distribution creates an electric field in the conductor The equilibrium distribution is reached when the forces from the electric and magnetic fields cancel The equilibrium electric field produces a potential difference (emf) in the conductor + - + E FB + FE + E - Physics 212 Lecture 16, Slide 2

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 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) B. 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) Rotate picture by 90 o (top view) Bar a No force on charges No charge separation No E field No emf XXXXX a v. X + - B b F + F XXXXX Fa = 0 : 22 Fb = qv. B v Bar b Opposite forces on charges Charge separation E = v. B emf = EL = v. BL Physics 212 Lecture 16, Slide 3

A conducting bar (green) rests on two frictionless wires connected by a resistor as shown. Checkpoint 2 a Equivalent circuit Changing Area A B The C entire apparatus is placed in a uniform magnetic field pointing into D the screen, and the bar is given an initial velocity to the right. R I V The Rotate motion of the green bar picture bycreates 90 o a current through the bar A. going up A B. B going down XXXXX B + F XXXXX : 22 Bar F Fb = qv 0 B v 0 Opposite forces on charges Charge separation E = v 0 B emf = EL = v 0 BL Physics 212 Lecture 16, Slide 4

A conducting bar (green) rests on two frictionless wires connected by a resistor as shown. Checkpoint 2 b F Energy I External agent must exert force F to the right to maintain constant v 0 Changing Area A B The entire apparatus is placed in a uniform magnetic field pointing C into the screen, and the bar is given an initial velocity to the right. D The current through this bar results in a force on the bar A. A down B up B. C right C. D D. E left E. into the screen Preflight 5 This energy is dissipated in the resistor! Counterclockwise Current F points to left : 22 Physics 212 Lecture 16, Slide 5

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 v B=5 T Out of Screen Let’s step through this one Checkpoint 5 20 Physics 212 Lecture 16, Slide 6

L E + v t Only leading side has charge separation emf = BLv (cw current) - LE + t v Leading and trailing sides have charge separation emf = BLv – BLv = 0 (no current) - LE + 20 Only trailing side has charge separation emf = BLv (ccw current) v t Physics 212 Lecture 16, Slide 7

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 v B=5 T Out of Screen Checkpoint 5 20 Physics 212 Lecture 16, Slide 8

Changing B field 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 B - + B + v - B B I 20 Physics 212 Lecture 16, Slide 9

Generator: Changing Orientation On which legs of the loop is charge separated? A) B) C) D) 22 Top and Bottom legs only Front and Back legs only All legs None of the legs parallel to top and bottom legs Perpendicular to front and back legs Physics 212 Lecture 16, Slide 10

Generator: Changing Orientation L w At what angle q is emf the largest? (A) q = 0 (B) q = 45 o (C) q = 90 o (D) emf is same at all angles 22 Largest for q = 0 (v perp to B) =v Physics 212 Lecture 16, Slide 11

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 v + v 20 I X B Physics 212 Lecture 16, Slide 12

Putting it together Change Area of loop Change magnetic field through loop Change orientation of loop relative to B Faraday’s Law We will study this law in detail next time ! Physics 212 Lecture 16, Slide 13

Example Problem A rectangular loop (h=0. 3 m L=1. 2 m) with total resistance of 5 W 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? I v 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 Physics 212 Lecture 16, Slide 14

Example Problem A rectangular loop (h=0. 3 m L=1. 2 m) with total resistance of 5 W 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? I v h x L What is the direction of the B field produced by the wire in the region of the loop? A) Into the page B) Out of the page C) Left D) Right E) Up Physics 212 Lecture 16, Slide 15

Example Problem A rectangular loop (h=0. 3 m L=1. 2 m) with total resistance of 5 W 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 I v h x L What is the emf induced on the left segment? A) Top is positive B) Top is negative C) Zero Physics 212 Lecture 16, Slide 16

Example Problem A rectangular loop (h=0. 3 m L=1. 2 m) with total resistance of 5 W 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 I v h x L What is the emf induced on the top segment? A) left is positive B) left is negative C) Zero perpendicular to wire Physics 212 Lecture 16, Slide 17

Example Problem A rectangular loop (h=0. 3 m L=1. 2 m) with total resistance of 5 W 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 I v h x L What is the emf induced on the right segment? A) top is positive B) top is negative C) Zero Physics 212 Lecture 16, Slide 18

Example Problem A rectangular loop (h=0. 3 m L=1. 2 m) with total resistance of 5 W 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 I v h x L Which expression represents the emf induced in the left wire (A) (B) (C) Physics 212 Lecture 16, Slide 19

Example Problem A rectangular loop (h=0. 3 m L=1. 2 m) with total resistance of 5 W 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 I v h x L Which expression represents the emf induced in the right wire (A) (B) (C) Physics 212 Lecture 16, Slide 20

Example Problem A rectangular loop (h=0. 3 m L=1. 2 m) with total resistance of 5 W 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 I v h x L Which expression represents the total emf in the loop? (A) (B) (C) Physics 212 Lecture 16, Slide 21

Follow-Up A rectangular loop (h=0. 3 m L=1. 2 m) with total resistance of 5 W is moving away from a long straight wire carrying total current 8 amps. I B into page + + v I h x - L - What is the direction of the induced current? (A) Clockwise (B) Counterclockwise e. Left > e. Right Clockwise current Physics 212 Lecture 16, Slide 22

Follow-Up A rectangular loop (h=0. 3 m L=1. 2 m) with total resistance of 5 W is moving away from a long straight wire carrying total current 8 amps. B into page I What is the direction of the force exerted by the magnetic field on the loop? (A) UP (B) DOWN (C) LEFT (B) RIGHT (B) F = 0 h x I v L B into page I Total force from B Points to the left !! Physics 212 Lecture 16, Slide 23