1. Magnetism Alternating-Current Circuits

2. Alternating Current Generators
A coil of area A and N turns rotating with constant angular velocity in a uniform magnetic field produce a sinusoidal emf
Alternating current motor
Instead of mechanically rotating, we can apply an ac potential difference generated by other ac generator to the coil. This produces an ac current in the coil, and the magnetic field exerts forces on the wires producing a torque that rotaes the coil.

3. The magnetic field.
Magnetic forces on a moving charges.
Magnetic forces on a current element
Torques on current loops and magnets

4. The Magnetic Field Magnets
The Earth is a natural magnet with magnetic poles near the north and south geographic poles.

5. The Magnetic Field
Magnets
Does exist an isolated magnetic pole?
The SI units of magnetic field is the tesla [T]
Earth magnetic field is about 10-4 T
Powerful laboratory produce fields of 1 -2 T as maximum
1 Gauss [G] = 10-4 Tesla [T]

6. The Magnetic Field

7. The Magnetic Field. Magnetic force on a moving charge
A proton is moving in a region of crossed fields E = 2x105 N/C and B = 3000 G, as is showed in the figure. (a) What is the speed of the proton if it is no deflected. (b) If the electric field is disconnected, draw the path of the proton

8. The Magnetic Field. Magnetic force on a current element
In the case of a straight segment of length L

9. The Magnetic Field. Torques on Current loops and MagnetsB
A current-carrying loop experiences no net force in a uniforme magnetic field, but it does experience a torque that tends to twist the loop
A circular loop of radius 2 cm has 10 turns of wire and carries a current of 3 A. The axis of the loop makes an angle of 30º with a magnetic field of 8000 G. Find the magnitude of the torque on the loop.

10. Sources of Magnetic Field
The Magnetic Field of Moving Charges
The Magnetic Field of Currents. The Biot- Savart Law
The Magnetic Field Due to a Current loop

11. Sources of Magnetic Field
Moving Point Charges are the source of Magnetic Field

12. Sources of Magnetic Field
A solenoid is a wire tightly wounded into a helix of closely space turns . A solenoid is used to produce a strong, unifrom magnetic field in the region surrounded by the loops
Inside a long solenoid
Find the magnetic field at the center of a solenoid of 600 turns that carries a current of 4 A

13. Sources of Magnetic Field: Solenoid and magnets
Left: Magnetic field lines of a solenoid; right Magnetic field lines of a bar magnet

14. Magnetic Induction
Magnetic Flux
Induced EMF and Faraday´s Law
Lenz´s Law

15. MAGNETIC INDUCTION
The induced emf is in such direction as to oppose, or tend to oppose, the change that produces it Lenz´s Law

18. Alternating Current Generators
A coil of area A and N turns rotating with constant angular velocity in a uniform magnetic field produce a sinusoidal emf
Alternating current motor
Instead of mechanically rotating, we can apply an ac potential difference generated by other ac generator to the coil. This produces an ac current in the coil, and the magnetic field exerts forces on the wires producing a torque that rotaes the coil.

19. 29-2 Alternating Current in a Resistor

27. 29-3 Alternating Current Circuits

34. 29-4 Phasors

37. 29-5 LC and RLC Circuits Without a Generator

44. 29-6 Driven RLC Circuits

59. 29-7 The Transformer

62. Problems