Applications of Electromagnetism in the News
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Transcript of Applications of Electromagnetism in the News
Copyright © 2012 Pearson Education Inc.
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
Copyright © 2012 Pearson Education Inc.
PowerPoint® Lectures forUniversity Physics, Thirteenth Edition – Hugh D. Young and Roger A. Freedman
Lectures by Wayne Anderson
Chapter 28
Sources of Magnetic Field
Copyright © 2012 Pearson Education Inc.
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
Copyright © 2012 Pearson Education Inc.
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
Copyright © 2012 Pearson Education Inc.
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=qQNpucos9wc
CERNTV. 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
Copyright © 2012 Pearson Education Inc.
The magnetic field of a moving charge
• A moving charge generates a magnetic field at some point in space around it.
Charge q, moving with speed v in a
direction
Point P in space some
distance away
q
v
Copyright © 2012 Pearson Education Inc.
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.
Charge q, moving with speed v in a
direction
Point P in space some
distance awayq
v
B(r)
r
Copyright © 2012 Pearson Education Inc.
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.
Charge q, moving with speed v in a
direction
Point P in space some
distance awayq
v
B(r)
r
• B = (0/4 q(v sin)/r2
Copyright © 2012 Pearson Education Inc.
The magnetic field of a moving charge
• A moving charge generates a magnetic field that depends on the velocity of the charge.
Copyright © 2012 Pearson Education Inc.
The magnetic field of a moving charge
• A moving charge generates a magnetic field that depends on the velocity of the charge.
• B = (0/4 q(v x r)/r3
= (0/4 q(v x r)
r2
Copyright © 2012 Pearson Education Inc.
Magnetic force between moving protons
• What is 0 ?
• Magnetic “Permeability” of free space
• Like a magnetic dielectric?
• Related to electric permittivity of free space 0
• Remember:
B fields ~ PermeaBility
E field ~ Voltage Difference ~ PermittiVity
Copyright © 2012 Pearson Education Inc.
Magnetic force between moving protons
• What is 0 ?
00 = 1/c2
• Magnitude = 0 = 4 x 10-7
• Units = Tesla-meters/Amp (T-m/A) or Webers/Amp-meter (Wb/A-m)
Copyright © 2012 Pearson Education Inc.
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
Copyright © 2012 Pearson Education Inc.
Force on UPPER proton?
• E field direction? (+y)
• F (E field) = q2/40r2
• F (B field) = qv x B
(from lower particle)
• B field direction? (+z)
• B = (0/4 q(vi x j)/r2
• FB = (0/4q2v2/r2
• F direction? (+y)
Copyright © 2012 Pearson Education Inc.
Ratio of Forces on UPPER proton?
• F (B field) / F (E field)
00v2
= v2/c2
At slow speeds, v <<c
FB <<FE
Copyright © 2012 Pearson Education Inc.
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!
Copyright © 2012 Pearson Education Inc.
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!
Copyright © 2012 Pearson Education Inc.
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 = (0/4 I(dl x r)/r2
Copyright © 2012 Pearson Education Inc.
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 = (0/4 I(dl x r)/r2
Copyright © 2012 Pearson Education Inc.
Magnetic field of a straight current-carrying conductor
• Law of Biot & Savart to a long straight conductor:
• B = 0I/2πx.
Copyright © 2012 Pearson Education Inc.
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?
Copyright © 2012 Pearson Education Inc.
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 = 0/4 I◦dl /r2
(-z direction)
For P2
B = 0/4 I ◦ dl ◦ sin (30) /r2 (also -z direction)
For P1:B =
xz
For P2:B =
xz
Copyright © 2012 Pearson Education Inc.
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 = 0I/2r
• r = 0I/2B = 4 mm!
Copyright © 2012 Pearson Education Inc.
Magnetic fields of long wires
• Example 28.4 for two wires. Find B at P1, P2, and P3.
Copyright © 2012 Pearson Education Inc.
Magnetic fields of long wires
• P1: - 0I/2d) + 0I/2(4d) = -0I/8d
• P2: +0I/2d) + 0I/2(d) = +0I/d
• P3: + 0I/2d) - 0I/2(d) = -0I/3d
Copyright © 2012 Pearson Education Inc.
Force between parallel conductors
• The force per unit length on each conductor is F/L = 0IIL/2πr.
• The conductors attract each other if the currents are in the same direction and repel if they are in opposite directions.
Copyright © 2012 Pearson Education Inc.
Forces between parallel wires
• Example 28.5: What force does each wire exert on the other?
• F/L = 0I I’/2r
• F/L = 1.0 x 104 N/m
Copyright © 2012 Pearson Education Inc.
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.
Copyright © 2012 Pearson Education Inc.
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.
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Ampere’s law (special case)
• Ampere’s law for a circular path around a long straight conductor.
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Ampere’s law (general statement)
• General statement of Ampere’s law
Copyright © 2012 Pearson Education Inc.
Ampere’s law (general statement)
• General statement of Ampere’s law
Copyright © 2012 Pearson Education Inc.
Ampere’s law (general statement)
• General statement of Ampere’s law
Copyright © 2012 Pearson Education Inc.
Magnetic fields of long conductors
• Example 28.7 for a long straight conductor.
• Example 28.8 for a long cylinder.
Copyright © 2012 Pearson Education Inc.
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.
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Field of a toroidal solenoid
• A toroidal solenoid is a doughnut-shaped solenoid.
• Follow Example 28.10 using Figure 28.25 below.
Copyright © 2012 Pearson Education Inc.
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.
Copyright © 2012 Pearson Education Inc.
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.