Ch. 21 - Magnetic Forces and Fields

1. Ch. 21 - Magnetic Forces and Fields

2. 3 D- visualization of vectors and current

3. 21.1 Magnetic Fields The needle of a compass is permanent magnet that has a north magnetic pole (N) at one end and a south magnetic pole (S) at the other.

4. 21.1 Magnetic Fields The behavior of magnetic poles is similar to that of like and unlike electric charges.

5. 21.1 Magnetic Fields Surrounding a magnet there is a magnetic field, an “alteration of space” caused by the magnet. The direction of the magnetic field at any point in space is the direction indicated by the north pole of a small compass needle placed at that point. The variable we use for the magnetic field is B.

6. 21.1 Magnetic Fields The magnetic field lines and pattern of iron filings in the vicinity of a bar magnet and the magnetic field lines in the gap of a horseshoe magnet.

7. 21.1 Magnetic Fields The iron core of the earth acts as a magnet and the earth has a magnetic field as shown below

8. 21.2 The Force That a Magnetic Field Exerts on a Charge Recall that when a charge is placed in an electric field, it experiences a force, according to The direction of the force is always parallel to or 180° from the direction of the field.

9. Magnetic Force on a moving charge due to an external magneticB field • A moving charge is a magnet. • In the presence of an external magnetic field, the charge will experience a force and change its speed and direction. • The magnetic field (B) is coming out of the page in this picture.

10. 21.2 The Force That a Magnetic Field Exerts on a Charge Right Hand Rule No. 1. Extend the right hand so the fingers point along the direction of the magnetic field and the thumb points along the velocity of the charge. The palm of the hand then faces in the direction of the magnetic force that acts on a positive charge. If the moving charge is negative, the direction of the force is opposite to that predicted by RHR-1.

11. Magnetic Force on a charge moving in a magnetic field (B) • The magnitude,|Fm|= qvB(sinθ) where θ is the angle between the direction of motion and the direction of B • The direction of Fm is given by RHR1 • The unit of B is the Tesla (Newton/Amp-meter) F = 0F<FmaxF = Fmax and is often used when studying the magnetic field of the Earth

12. Magnetic Force on a moving charge due to an external B field Fm = qvBsinθ • Only a moving charge experiences a force. • There must be a component of velocity perpendicular to the external field, or F = 0.

13. Magnetic Force on a moving charge due to an external B field Fm = qvBsinθ • The force is mutually perpendicular to v and B. • The force on a negative moving charge is shown by the left hand rule!

14. Conceptual Problem A positive charge is traveling in the direction shown by the arrow. It enters the external B field (dots mean out of the page). The particle experiences a force: a. to the right b. to the left c. into the page d. out of the page

15. Conceptual Problem A positive charge is traveling in the direction shown by the arrow. It enters the external B field (dots mean out of the page). The particle experiences a force: a. to the right b. to the left c. into the page d. out of the page

16. Numerical problem A particle with a charge of +8.4 μC and a speed of 45 m/s in the direction shown (purple) enters an external magnetic field (red) of 0.30 T. Find the magnitude and the direction of the magnetic force on the particle.

17. Numerical problem A particle with a charge of +8.4 μC and a speed of 45 m/s in the direction shown(purple) enters an external magnetic field (red) of 0.30 T. Find the magnitude and the direction of the magnetic force on the particle. Note that vy = v sin 150° is the component perpendicular to the magnetic field. Answer: 5.67 x 10-5 Newtons, into the page vy

18. 21.3 The Motion of a Charged Particle in a Magnetic Field • The magnetic force always remains perpendicular to the velocity and is directed toward the center of the circular path. • The magnetic force results in a centripetal acceleration. According to Newton’s Law:

19. 21.4 The Mass Spectrometer Chemists and biologists use the “mass spec” to identify the the mass and/or charge of molecules.

20. 21.4 The Mass Spectrometer The mass spectrum of naturally occurring neon, showing three isotopes.

21. How much Deuterium in my sample? Deuterium, (“heavy hydrogen”) has an extra neutron in its nucleus. Researchers want to know the percentage of deuterium in a sample of hydrogen. The hydrogen is ionized and then is accelerated through the metal plates with a potential difference of 2100 V It then enters a uniform B field 0.1T, into the page. Ignore effects due to gravity. At what radius should the detector be placed? mp = mn = 1.67 x 10-27 kg q = e = 1.60 x 10-19 C We need to use both Conservation of Energy and Newton’s Law for uniform circular motion to solve this problem.

22. How much Deuterium in my sample? 1. find the speed of the particle upon exiting the capacitor, using conservation of energy: EPE0 = KEf q ∆V = mv2/2, v = 4.49 x 105 m/s. 2. Use Newton’s Law to find an expression for r: r = 9.37 x 10-4 m

23. Ranking Task a. 3,2,1 c. 2,3,1 b. 3,1,2 d.1,3,2 e. 1,2,3 3 particles move perpendicular to a uniform B field and travel in circular paths as shown. They have the same mass and speed. Rank the particles in order of charge magnitude, greatest to least:

24. Ranking Task a. 3,2,1 c. 2,3,1 b. 3,1,2 d.1,3,2 e. 1,2,3 charge and radius are inversely proportional 3 particles move perpendicular to a uniform B field and travel in circular paths as shown. They have the same mass and speed. Rank the particles in order of charge magnitude, greatest to least:

25. 21.5 The Force on a Current in a Magnetic Field The magnetic force on the moving charges pushes the wire to the right.

26. 21.5 The Force on a Current in a Magnetic Field

27. 21.6 The Torque on a Current-Carrying Coil The two forces on the loop have equal magnitude but an application of RHR-1 shows that they are opposite in direction.

28. 21.6 The Torque on a Current-Carrying Coil The loop tends to rotate such that its normal becomes aligned with the magnetic field.

29. 21.6 The Torque on a Current-Carrying Coil number of turns of wire

30. What happens to the loop? The magnetic field exerts: a. a net force and a net torque b. a net force but no net torque c. a net torque, but no net force d. neither a net force, nor a net torque

31. What happens to the loop? The magnetic field exerts: a. a net force and a net torque b. a net force but no net torque c. a net torque, but no net force d. neither a net force, nor a net torque

32. What happens to this loop? B = 0.25T, I = 12 A Single turn square with sides of 0.32m length Part 1: Is there a torque? a. yes, top out of the page, bottom into the page b. yes, left side out of the page, right side into the page c. no torque

33. What happens to this loop? B = 0.25T, I = 12 A Single turn square with sides of 0.32m length Part 1: Is there a torque? a. yes, top out of the page, bottom into the page b. yes, left side out of the page, right side into the page c. no torque

34. What happens to this loop? B = 0.25T, I = 12 A Single turn square with sides of 0.32m length Part 2: What is the magnitude of the torque?

35. What happens to this loop? B = 0.25T, I = 12 A Single turn square with sides of 0.32m length Part 2: What is the magnitude of the torque? = F(L/2)top + F(L/2)bottom Or = NIAB = 30.7 N-m

36. 21.6 The Torque on a Current-Carrying Coil • Example 6 The Torque Exerted on a Current-Carrying Coil • A coil of wire has an area of 2.0x10-4m2, consists of 100 loops or turns, • and contains a current of 0.045 A. The coil is placed in a uniform magnetic • field of magnitude 0.15 T. (a) Determine the magnetic moment of the coil. • Find the maximum torque that the magnetic field can exert on the • coil. (a) (b)

37. 21.6 The Torque on a Current-Carrying Coil The basic components of a dc motor.

38. 21.6 The Torque on a Current-Carrying Coil

39. 21.7 Magnetic Fields Produced by Currents Right-Hand Rule No. 2. Curl the fingers of the right hand into the shape of a half-circle. Point the thumb in the direction of the conventional current, and the tips of the fingers will point in the direction of the magnetic field.

40. 21.7 Magnetic Fields Produced by Currents A LONG, STRAIGHT WIRE permeability of free space

41. 21.7 Magnetic Fields Produced by Currents Example 7 A Current Exerts a Magnetic Force on a Moving Charge The long straight wire carries a current of 3.0 A. A particle has a charge of +6.5x10-6 C and is moving parallel to the wire at a distance of 0.050 m. The speed of the particle is 280 m/s. Determine the magnitude and direction of the magnetic force on the particle.

42. 21.7 Magnetic Fields Produced by Currents

43. 21.7 Magnetic Fields Produced by Currents Current carrying wires can exert forces on each other.

44. 21.7 Magnetic Fields Produced by Currents Conceptual Example 9 The Net Force That a Current-Carrying Wire Exerts on a Current Carrying Coil Is the coil attracted to, or repelled by the wire?

45. 21.7 Magnetic Fields Produced by Currents A LOOP OF WIRE center of circular loop

46. 21.7 Magnetic Fields Produced by Currents Example 10 Finding the Net Magnetic Field A long straight wire carries a current of 8.0 A and a circular loop of wire carries a current of 2.0 A and has a radius of 0.030 m. Find the magnitude and direction of the magnetic field at the center of the loop.

47. 21.7 Magnetic Fields Produced by Currents

48. 21.7 Magnetic Fields Produced by Currents The field lines around the bar magnet resemble those around the loop.

49. 21.7 Magnetic Fields Produced by Currents

50. 21.7 Magnetic Fields Produced by Currents A SOLENOID number of turns per unit length Interior of a solenoid