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


PowerPoint® Lectures forUniversity Physics, Thirteenth Edition – Hugh D. Young and Roger A. Freedman

Lectures by Wayne Anderson

Chapter 28

Sources of Magnetic Field


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


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


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


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



• The field direction at that point depends upon the directions of the velocity vector AND the relative location of the point in space.


direction


distance awayq

v

B(r)

r



• 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.


direction


distance awayq

v

B(r)

r

• B = (0/4 q(v sin)/r2



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


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


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)


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


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)


Ratio of Forces on UPPER proton?

• F (B field) / F (E field)

00v2

= v2/c2

At slow speeds, v <<c

FB <<FE


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!




• So a current of moving charges creates a B field!




• The law of Biot and Savart

• dB = (0/4 I(dl x r)/r2




• The law of Biot and Savart

• dB = (0/4 I(dl x r)/r2


Magnetic field of a straight current-carrying conductor

• Law of Biot & Savart to a long straight conductor:

• B = 0I/2πx.


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?


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


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!



• Example 28.4 for two wires. Find B at P1, P2, and P3.



• P1: - 0I/2d) + 0I/2(4d) = -0I/8d

• P2: +0I/2d) + 0I/2(d) = +0I/d

• P3: + 0I/2d) - 0I/2(d) = -0I/3d


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.


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


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.


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.


Ampere’s law (special case)

• Ampere’s law for a circular path around a long straight conductor.


Ampere’s law (general statement)

• General statement of Ampere’s law








Magnetic fields of long conductors

• Example 28.7 for a long straight conductor.

• Example 28.8 for a long cylinder.


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.


Field of a toroidal solenoid

• A toroidal solenoid is a doughnut-shaped solenoid.

• Follow Example 28.10 using Figure 28.25 below.


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.


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.


Hysteresis

• Read the text discussion of hysteresis using Figure 28.29 below.

• Follow Example 28.12.

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Applications of Electromagnetism in the News