Electricity from magnetism

1. Electricity from magnetism Chapter 20, section 1

2. objectives • Recognize that relative motion between a conductor and a magnetic field induces an emf in the conductor. • Describe how the change in the number of magnetic field lines through a circuit loop affects the magnitude and direction of the induced electric current

3. objectives • Apply Lenz’s law and Faraday’s law of induction to solve problems involving induced emf and current.

4. Electromagnetic induction Electromagnetic Induction – the process of creating a current in a circuit loop by changing the magnetic flux in the loop. Figure 1 When the circuit loop crosses the lines of the magnetic field, a current is induced in the circuit, as indicated by the movement of the galvanometer.

5. Electromagnetic induction * Consider a closed circuit consisting of only a resistor that is in the vicinity of a magnet. There is no battery to supply a current. If neither the magnet nor the circuit is moving with respect to the other, no current will be present in the circuit. But, if the circuit moves toward or away from the magnet or the magnet moves toward or away from the circuit, a current is induced.

6. The separation of charges by the magnetic force induces an emf. • The separation of positive and negative moving charges by the magnetic force creates a potential difference (emf) between the ends of the conductor. (See Figure 2, p.709)

7. The angle between a magnetic field and a circuit affects induction. • One way to induce an emf in a closed loop of wire is to move all or part of the loop into or out of a constant magnetic field. • No emf is induced if the loop is static and the magnetic field is constant.

8. The angle between a magnetic field and a circuit affects induction. • The induced emf and current are: • largest, when the plane of the loop is perpendicular to the magnetic field; • smaller, when the plane of the loop is tilted into the magnetic field; • zero, when the plane of the loop and the magnetic field are parallel

9. Change in the number of magnetic field induces a current. • Changing the size of the circuit loop or rotating the loop changes the number of field lines passing through the loop, as does changing the magnetic field’s strength or direction.

10. Ways of inducing a current in a circuit • (Copy Table 1, page 710) • Circuit is moved into or out of magnetic field (either circuit or magnet moving). • Circuit is rotated in the magnetic field (angle between area of circuit and magnetic field changes). • Intensity and/or direction of magnetic field is varied.

11. Conceptual challenge • Homework: Answer in your notebook, page 711.

12. Lenz’s law • Heinrich Emil Lenz’s law states that: “The magnetic field of the induced current is in a direction to produce a field that opposes the change causing it.” Note: The field of the induced current does not oppose the applied field but rather the change in the applied field.

13. Faraday’s law • Michael Faraday’s law of induction predicts the magnitude of the induced emf. • Faraday' s law is not an explanation of Induction but merely a description of what induction is.

14. Faraday’s Law of Magnetic Induction average induced emf = – the number of loops in the circuit x the time rate of change of the magnetic flux

15. Faraday’s Law of Magnetic Induction Alternative formula: or Where: A = circuit area B = applied magnetic field strength θ = angle of orientation

16. Sample problem • A coil with 25 turns of wire is wrapped around a hollow tube with an area of 1.8 sq.m. Each turn has the same area as the tube. A uniform magnetic field is applied at a right angle to the plane of the coil. If the field increases uniformly from 0.00 T to 0.55 T in 0.85 s, find the magnitude of the induced emf in the coil. If the resistance in the coil is 2.5 Ω, find the magnitude of the induced current in the coil.

17. Sample problem • Answer: emf = -29.12 V , approx. 29 V I = -11.65 A, approx. 12 A

18. Practice exercises • A coil with 25 turns of wire is moving in a uniform magnetic field of 1.5 T. The magnetic field is perpendicular to the plane of the coil. The coil has a cross-sectional area of 0.80 sq.m. The coil exits the field in 1.0 s. • Find the induced emf. • Determine the induced current if the coil’s resistance is 1.5 Ω.

19. Practice exercises • Answer: a. 30 V b. 20 A

20. Practice exercises 2. Solve Practice A exercises, page 714. 3. Solve Section Review, no. 3, page 715.

21. Practice exercises • Answers: Practice A • emf = 0.30 V • I = 14 A • emf = 0.14 V • B = 4.83 x 10^(-5) T Section Review 3. emf = 0.21 V