Physics 2112 Unit 16 Concept: Motional EMF

Really odd formula coming: The Plan Really odd formula coming: Spend a bit of time seeing that it makes sense (See prelecture for additional info.) Do two examples problem in detail. Move on to use formula.

Motional EMF Motion of a conductor through B field can cause potential difference. (Remember Hall Effect clicker question?) B X X X X X X X X + - F X X X X X X X X + - + - E + - E FB FE X X X X X X X X v X X X X X X X X X X X X X X X X L

CheckPoint 1 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 Which of the following statements is true? A motional emf exists in the bar for case (a), but not for case (b) A motional emf exists in the bar for case (b), but not for case (a) A motional emf exists in the bar for both cases (a) and (b) A motional emf exists in the bar for neither case (a) nor case (b)

CheckPoint 2A A conducting bar (green) rests on two frictionless wires connected by a resistor as shown. 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. x x x x x x x x The motion of the green bar creates a current through the bar going up going down

CheckPoint 2b A conducting bar (green) rests on two frictionless wires connected by a resistor as shown. 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. x x x x x x x x The current through this bar results in a force on the bar down up right left into the screen out of the screen

Example 16.1 A 10cm conducting bar (green) rests on two frictionless wires connected by a resistor R = 50W. The entire apparatus is placed in a uniform magnetic field of 0.5 T pointing into the screen. x x x x x x x x The bar is pulled to the right by a force, F, at a velocity of 8m/sec. What is the current through the resistor? What is the force required to keep the bar moving at this constant velocity?

Checkpoint 2 x x x x x x x x 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 of the field on the right side.

Checkpoint 3 A conducting rectangular loop moves with velocity v towards an infinite straight wire carrying current as shown. In what direction is the induced current in the loop? clockwise counterclockwise There is no induced current in the loop

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 Parallel to top and bottom legs Perpendicular to front and back legs

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

Checkpoint 4 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? from b to a from a to b There is no induced current in the loop at this time

Example 16.2 (Loop moving from wire) A rectangular loop (h = 0.3m L = 1.2 m) with total resistance of 5W is moving away from a long straight wire at a velocity of 9 m/sec. The wire carries 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

Net Force on the loop B into page Note that the loop is moving with a constant velocity.  Fnet = 0. What are the magnetic forces on the four edges of the loop? I v I h x L Something must be doing positive work on the loop to keep it moving at constant v.

Faraday’s Law Putting it Together Notice the minus sign!!! Change Area of loop Change magnetic field through loop Change orientation of loop relative to B Faraday’s Law Notice the minus sign!!!