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Applications of Electromagnetism in the News

Applications of Electromagnetism in the News. New battery technology Summer, Lauren (2013, November 1) Silicon Valley in Race for Battery Breakthrough KQED Science . http://blogs.kqed.org/science/audio/silicon-valley-in-race-for-battery-breakthrough/ Understanding Earth’s Magnetic Field

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Applications of Electromagnetism in the News

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  1. Applications of Electromagnetism in the News • New battery technology • Summer, Lauren (2013, November 1) Silicon Valley in Race for Battery Breakthrough KQED Science. http://blogs.kqed.org/science/audio/silicon-valley-in-race-for-battery-breakthrough/ • Understanding Earth’s Magnetic Field • Redd, N. (2013, October 9) Weird Shift of Earth's Magnetic Field Explained. Space.com. http://www.space.com/23131-earth-magnetic-field-shift-explained.html

  2. Chapter 28 Sources of Magnetic Field

  3. Goals for Chapter 28 • To determine the magnetic field produced by a moving charge • To study the magnetic field of an element of a current-carrying conductor • To calculate the magnetic field of a long, straight, current-carrying conductor

  4. Goals for Chapter 28 • To study the magnetic force between current-carrying wires • To determine the magnetic field of a circular loop • To use Ampere’s Law to calculate magnetic fields

  5. Introduction • What can we say about the magnetic field due to a solenoid? • What actually creates magnetic fields? • We will introduce Ampere’s law to calculate magnetic fields. Check out CERN. The Large Hadron Collider (LHC). 2008. YouTube. Accessed 10/29/12 from http://www.youtube.com/watch?v=qQNpucos9wcCERNTV. The Large Hadron Collider. 2008. YouTube. Accessed 10/19/12 from http://www.youtube.com/watch?v=UDoIzvKumGI&feature=related Euronews. Large Hadron Collider: A racetrack for particles. (2011) YouTube. Accessed 10/28/12 from http://www.youtube.com/watch?v=9kU-WsH9cO8

  6. The magnetic field of a moving charge • A moving charge generates a magnetic field at some point in space around it. Point P in space some distance away Charge q, moving with speed v in a direction q v

  7. The magnetic field of a moving charge • The field direction at that point depends upon the directions of the velocity vector AND the relative location of the point in space. B(r) Point P in space some distance away r q Charge q, moving with speed v in a direction v

  8. The magnetic field of a moving charge • The field strength at that point depends on the speed and amount of the charge, the distance to the point, and the angle between v and r. B(r) • B = (m0/4p) q(v sina)/r2 Point P in space some distance away r a q Charge q, moving with speed v in a direction v

  9. The magnetic field of a moving charge • A moving charge generates a magnetic field that depends on the velocity of the charge.

  10. The magnetic field of a moving charge • A moving charge generates a magnetic field that depends on the velocity of the charge. • B = (m0/4p) q(v x r)/r3 = (m0/4p) q(v x r) r2

  11. Magnetic force between moving protons • What is m0 ? • Magnetic “Permeability” of free space • Like a magnetic dielectric? • Related to electric permittivity of free space e0 • Remember: B fields ~ PermeaBilityE field ~ Voltage Difference ~ PermittiVity

  12. Magnetic force between moving protons • What is m0 ? • m0e0 = 1/c2 • Magnitude= m0 = 4p x 10-7 • Units= Tesla-meters/Amp (T-m/A) or Webers/Amp-meter (Wb/A-m)

  13. Ex 28.1 Magnetic force between moving protons • E field exists moving or not! • B Field of one moving particle creates FORCE on another moving particle

  14. Force on UPPER proton? • E field direction? (+y) • F(E field) = q2/4pe0r2 • F(B field) = qv x B(from lower particle) • B field direction? (+z) • B= (m0/4p)q(vix j)/r2 • FB = (m0/4p)q2v2/r2 • F direction? (+y)

  15. Ratio of Forces on UPPER proton? • F(B field) /F(E field) • = e0m0v2 • = v2/c2 • At slow speeds, v <<c • FB <<FE

  16. Magnetic field of a current element • The total magnetic field of several moving charges is the vector sum of each field. • So a current of moving charges creates a B field!

  17. Magnetic field of a current element • The total magnetic field of several moving charges is the vector sum of each field. • So a current of moving charges creates a B field!

  18. Magnetic field of a current element • The total magnetic field of several moving charges is the vector sum of each field. • The law of Biot and Savart • dB = (m0/4p) I(dl x r)/r2

  19. Magnetic field of a current element • The total magnetic field of several moving charges is the vector sum of each field. • The law of Biot and Savart • dB = (m0/4p) I(dl x r)/r2

  20. Magnetic field of a straight current-carrying conductor • Law of Biot & Savart to a long straight conductor: • B = 0I/2πx.

  21. Magnetic field of a current segment • Example 28.2: What is B field of 125 Amp current from 1.0 cm segment of wire 1.2 meters away at two points?

  22. Magnetic field of a current segment • Example 28.2: What is B field of 125 Amp current from 1.0 cm segment of wire 1.2 meters away at two points? For P1:B = m0/4p I◦dl /r2(-z direction) For P1:B = -8.7 x 10-8 T (z) For P2B = m0/4p I ◦ dl ◦ sin (30) /r2(also -z direction) For P2:B = -4.3 x 10-8 T (z)

  23. Magnetic fields of long wires • Example 28.3 for one wire. • Long, straight conductor carries 1.0 A; • Where does B = 0.5 x 10-4 T (about the equivalent of Earth’s field)? • B = 0.5 x 10-4 T = m0I/2pr • r = m0I/2pB = 4 mm!

  24. Magnetic fields of long wires • Example 28.4 for two wires. Find B at P1, P2, and P3.

  25. Magnetic fields of long wires • P1: - m0I/2p(2d) + m0I/2p(4d) = -m0I/8pd • P2: +m0I/2p(d) + m0I/2p(d) = +m0I/pd • P3: + m0I/2p(3d) - m0I/2p(d) = -m0I/3pd

  26. Force between parallel conductors • The force per unit length on each conductor is F/L = 0IIL/2πr. • The conductors attract each other if the currents are in the same direction and repel if they are in opposite directions.

  27. Forces between parallel wires • Example 28.5: What force does each wire exert on the other? • F/L = m0II’/2pr • F/L = 1.0 x 104 N/m

  28. Magnetic field of a circular current loop • The Biot Savart law gives Bx = 0Ia2/2(x2 + a2)3/2 on the axis of the loop. • At the center of N loops, where x = 0, the field on the axis is Bx = 0NI/2a.

  29. Magnetic field of a coil • Figure 28.13 (top) shows the direction of the field using the right-hand rule. • Figure 28.14 (below) shows a graph of the field along the x-axis.

  30. Ampere’s law (special case) • Ampere’s law for a circular path around a long straight conductor.

  31. Ampere’s law (general statement) • General statement of Ampere’s law

  32. Ampere’s law (general statement) • General statement of Ampere’s law

  33. Ampere’s law (general statement) • General statement of Ampere’s law

  34. Magnetic fields of long conductors • Example 28.7 for a long straight conductor. • Example 28.8 for a long cylinder.

  35. Field of a solenoid • A solenoid consists of a helical winding of wire on a cylinder. • Follow Example 28.9 using Figures 28.22–28.24 below.

  36. Field of a toroidal solenoid • A toroidal solenoid is adoughnut-shaped solenoid. • Follow Example 28.10 using Figure 28.25 below.

  37. The Bohr magneton and paramagnetism • Follow the text discussions of the Bohr magneton and paramagnetism, using Figure 28.26 below. • Table 28.1 shows the magnetic susceptibilities of some materials. • Follow Example 28.11.

  38. Diamagnetism and ferromagnetism • Follow the text discussion of diamagnetism and ferromagnetism. • Figure 28.27 at the right shows how magnetic domains react to an applied magnetic field. • Figure 28.28 below shows a magnetization curve for a ferromagnetic material.

  39. Hysteresis • Read the text discussion of hysteresis using Figure 28.29 below. • Follow Example 28.12.

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