Induced EMF and Induced Current

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1 Induced EMF and Induced Current 1

2 Notice: There is NO BATTERY in the secondary circuit! It is the changing field that produces the current. ΔB I 2

3 The current in the coil is called the induced current because it is brought about by a changing magnetic field. Since a source emf is always needed to produce a current, the coil behaves as if it were a source of emf. This emf is known as the induced emf. 3

An emf can be induced by changing the area of a coil in a constant magnetic field. ΔA I In each example, both an emf and a current are induced because the coil is part of a complete circuit.

4 An emf can be induced by changing the area of a coil in a constant magnetic field. ΔA I In each example, both an emf and a current are induced because the coil is part of a complete circuit. If the circuit were open, there would be no induced current, but there would be an induced emf. The phenomena of producing an induced emf with the aid of a magnetic field is called electromagnetic induction. 4

5 Motional Emf THE EMF INDUCED IN A MOVING CONDUCTOR F B = q v x B Notice that as this rod moves, charges separate, and an emf is induced in the rod. The separated charges on the ends of the conductor give rise to an induced emf, called a motional emf. If you stop moving, you stop the emf. From where is this energy coming? answer: 5

6 Motional Emf calculating motional emf : Motional emf when v, B, and L are mutually perpendicular E = v B L (really: E = v x B L) (on formula sheet) 6

7 Motional Emf 2. Near San Francisco, where the vertically downward component of the earth's magnetic field is 4.8 x 10 5 T, an emf of 2.4 x 10 3 V is induced between the sides of the car. (a) Which side of the car is positive (driver's or passengers)? (b) What is the width of the car? 7

8 Motional Emf 5. The drawing shows three identical rods (A, B, and C) moving in different planes. A constant magnetic field of magnitude 0.45 T is directed along the +y axis. The length of each rod is L = 1.3 m, and the rods each have the same speed, v a = v b = v c = 2.7 m/s. For each rod, find the magnitude of the motional emf, and indicate which end (1 or 2) of the rod is positive. 8

9 Motional Emf R = 0.75 Ω B = 0.50 T v = 4.0 m/s L = 1.3 m 9

10 Motional Emf MOTIONAL EMF AND ELECTRICAL ENERGY Lighting this bulb isn't free! In order to keep the rod moving at constant velocity, the force the hand exerts on the rod must balance the magnetic force on the current: F hand = F B = ILB 10

11 answer: Magnetic Flux! Do you know a name for this quantity? E Hint: This quantity has to do with the amount of field lines going through an area. 11

12 E E = ΔΦB Δt * (on formula sheet) * Usually you'll see this written with a " " sign before it. That negative sign says that the direction of the current induced in the circuit is such that the magnetic force acts on the rod to oppose its motion and slow it down. Better way to write this: E = ΔΦB Δt Don't let the elegance of this fool you; this is the most sublime and profound things human beings have ever discovered! 12

13 Electric Flux (flow) Measure of how much of the electric field penetrates (flows through) a given surface. Remember this: Electric flux is proportional to the number of electric field lines going through a surface or area. Smaller Flux Bigger Flux The flux is proportional to the strength of the field. 13

14 Smaller Flux Bigger Flux The flux is proportional to the area of the surface. 14

15 The flux is also proportional to how the area is oriented. Θ A E Area is quantified as vector that points perpendicular to the surface, and is as large as the surface area of the surface. For which angle of Θ do you get the most flux through a given surface area? Would this be a cross product or a dot product idea? 15

16 Calculating Electric Flux ΦE = E A = E A cos Θ 16

17 Magnetic Flux Magnetic flux is defined the same way as electric flux. Magnetic flux is proportional to both the strength of the magnetic field passing through the plane of a loop of wire and the area of the loop. A A 17

18 Calculating Magnetic Flux ΦB = B A = B A cos Θ (on formula sheet, but they use φm) Units: T m 2 = Weber (Wb) Wilhelm Eduard Weber German 18

19 17. A five sided object, whose dimensions are shown in the drawing, is placed in a uniform magnetic field. The magnetic field has a magnitude of 0.25 T and points along the positive y direction. Determine the magnetic flux through each of the five sides. 19

Faraday s Law of Electromagnetic Induction Michael Faraday 1791 1867

20 Faraday s Law of Electromagnetic Induction Michael Faraday British Joseph Henry American The usefulness of this idea is obvious! 20

21 Faraday s Law of Electromagnetic Induction If a circuit contains N tightly wound loops and the flux changes by ΔΦ B during a time interval Δt, the average emf induced is given by Faraday s Law: E = N ΔΦB t Don't miss the Δ! Again, more profound than 99.9% of the ideas you've ever heard! 21

Faraday s Law of Electromagnetic Induction More on the Negative: E = N ΔΦB t Lenz's Law The current caused by the induced emf travels in the direction

22 Faraday s Law of Electromagnetic Induction More on the Negative: E = N ΔΦB t Lenz's Law The current caused by the induced emf travels in the direction that creates a magnetic field with flux opposing the change in the original flux through the circuit. Heinrich Friedrich Emil Lenz Russian 22

23 Example: The current in the wire is steadily increasing as time goes by. This induces a current in the rectangular loop. What direction does current flow in the rectangular loop? 23

24 Example: The north pole of the magnet moves toward the coil. What direction must the current flow in the coil? 24

25 Example: A coil of wire is placed near a solenoid. a) When the switch is closed, which way does current flow in the coil? b)what happens when the switch is reopened? 25

26 Caution: Some people mistakenly think that Lenz's Law says that the induced magnetic field is always counter to the external magnetic field. Example: The graph shows how magnetic field around a loop coil varies with time. Which way will the induced current flow in the coil? 26

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29 21. A circular coil (950 turns, radius m) is rotating in a uniform magnetic field. At t = 0, the normal to the coil is perpendicular to the magnetic field. At t = s, the normal makes an angle of Φ = 45 with the field because the coil has made one eighth of a revolution. An average emf of magnitude V is induced in the coil. Find the magnitude of the magnetic field at the location of the coil. 29

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Phys222 Winter 2012 Quiz 4 Chapters 29-31. Name

Phys222 Winter 2012 Quiz 4 Chapters 29-31. Name Name If you think that no correct answer is provided, give your answer, state your reasoning briefly; append additional sheet of paper if necessary. 1. A particle (q = 5.0 nc, m = 3.0 µg) moves in a region