Magnetic Fields and Electromagnetism

Chapter 24 and 26

Magnetism

• The word magnetism comes from the Greek word for a certain type of stone (lodestone) containing iron oxide found in Magnesia, a district in northern Greece.

• The Greeks and the Chinese found lodestone could exert forces on similar stones and could impart this property (magnetize) to a piece of iron it touched

• And that a small sliver of lodestone suspended with a string will always align itself in a north-south direction—it detects the earth’s magnetic field

• Use of magnets to aid in navigation can be traced back to at least the eleventh century

Magnetism - History• Not until 1819 was a connection

between electrical and magnetic phenomena shown. Danish scientist Hans Christian Oersted observed that a compass needle in the vicinity of a wire carrying electrical current was deflected!

• In 1831, Michael Faraday discovered that a momentary current existed in a circuit when the current in a nearby circuit was started or stopped

• Shortly thereafter, he discovered that motion of a magnet toward or away from a circuit could produce the same effect.

All magnetic phenomena result

from forces between electric charges in

motion.

NS

Magnetic Poles• Magnets have at least one north pole and

one south pole. By convention, we say that the magnetic field lines leave the North end of a magnet and enter the South end of a magnet.

• Like electric field lines, increased density indicates increased magnetic field.

• The ends of a magnet are where the magnetic effect is the strongest. These are called “poles.”

Magnetic Field Lines of a bar magnet

For every North, there is a South• Poles of a magnet always come in pairs!• Even an individual electron has a magnetic “dipole”!• Although there have been many searches for magnetic

monopoles—No monopoles have ever been found!• If you take a bar magnet and break it into two pieces, each

piece will again have a North pole and a South pole. If you take one of those pieces and break it into two, each of the smaller pieces will have a North pole and a South pole. No matter how small the pieces of the magnet become, each

piece will have a North pole and a South pole.

S N S N S N

Like poles repel; Unlike poles attract

Like repels like…Like repels like…

Opposites attract!Opposites attract!

The Earth is like a giant magnet!• The nickel iron core

of the earth gives the earth a magnetic field much like a bar magnet.

• The north pole of the compass magnet is attracted to the magnetic south pole of the Earth.

Magnetic Field Lines• Michael Faraday realized that a magnet has a

‘magnetic field’ distributed throughout the surrounding space

• Magnetic field lines describe the structure of magnetic fields in three dimensions. They are defined as follows: If at any point on such a line we place an ideal compass needle, free to turn in any direction (unlike the usual compass needle, which stays horizontal) then the needle will always point along the field line.

• Field lines converge where the magnetic force is strong, and spread out where it is weak.

• By convention, we say that the magnetic field lines leave the North end of a magnet and enter the South end of a magnet.

• Small pieces of iron or small compasses can be used to visualize the magnetic field Field Lines Around a Magnetic Sphere

Magnetic Fields• A stationary charge has an electric field around it; a moving charge has

an electric and a magnetic field around it and exerts a force on any other charge moving through the magnetic field.

• Magnetic fields are vector quantities….that is, they have a magnitude and a direction.

• Magnetic Field vectors as written as B or B• Direction of magnetic field at any point is defined as the direction of

motion of a charged particle on which the magnetic field would not exert a force.

• Magnitude of the B-vector is proportional to the force acting on the moving charge, magnitude of the moving charge, the magnitude of its velocity, and the angle between v and the B-field.

• Unit is the Tesla or the Gauss (1 T = 10,000 G).

Magnetic Domains• Understanding source of the

magnetic field generated by bar magnet lies in understanding currents at atomic level within bulk matter.

Orbits of electrons about nuclei

Intrinsic “spin” of electrons (more important effect)

• Magnetic substances like iron, cobalt, and nickel have unpaired spins, in these substances there can be small areas where the groups of atoms are aligned (unpaired spins “pointing in the same direction”). These regions of aligned atoms are called domains.

• All of the domains of a magnetic substance tend to align themselves in the same direction when placed in a magnetic field. These domains are typically composed of billions of atoms.

Magnetic Domains

Magnetic Materials• Materials can be classified by how they respond to an applied

magnetic field, Bapp.

• Paramagnetic (aluminum, tungsten, oxygen,…)• Atomic magnetic dipoles (~atomic bar magnets) tend to line up with

the field, increasing it. But thermal motion randomizes their directions, so only a small effect persists.

• Diamagnetic (gold, copper, water,…)• The applied field induces an opposing field; again, this is usually very

weak. [Exception: Superconductors exhibit perfect diamagnetism they exclude all magnetic fields]

• Ferromagnetic (iron, cobalt, nickel,…)• Somewhat like paramagnetic, the dipoles prefer to line up with the

applied field. But there is a complicated collective effect due to strong interactions between neighboring dipoles they tend to all line up the same way.

Ferromagnets• Even in the absence of an applied B, the dipoles tend to strongly align

over small patches – “domains”. Applying an external field, the domains align to produce a large net magnetization.

• “Soft” ferromagnets• The domains re-randomize when the field is removed

• “Hard” ferromagnets• The domains persist even when the field is removed• “Permanent” magnets

• Domains may be aligned in a different direction by applying a new field

• Domains may be re-randomized by sudden physical shock• If the temperature is raised above the “Curie point” (770˚ for

iron), the domains will also randomize paramagnet

MagneticDomains

How does a magnet attract screws, paper clips, refrigerators, etc., when they are not “magnetic”?

• The materials are all “soft” ferromagnets. The external field temporarily aligns the domains so there is a net dipole, which is then attracted to the bar magnet.- The effect vanishes with no applied B field- It does not matter which pole is used.

End of paper clipS N

Electromagnetism• When an electric current passes

through a wire a magnetic field is formed.

• When an electric current is passed through a coil of wire wrapped around a metal core, a very strong magnetic field is produced. This is called an electromagnet.

Indicating Direction of Magnetic Field

• If B is directed into the page we use crosses representing the tail of arrows indicating the direction of the field,

• If B is directed out of the page, we use dots.

• If B is in the page, we use lines with arrow heads.

x x x xx x x x x

x x x x x xx x x x xx x x x

. . . .. . . . .

. . . . . .. . . . .. . . .

Magnetic Field near a current-carrying wire

• In this diagram, the solid teal circle in the center represents a cross-section of a current-carrying wire in which the current is coming out of the plane of the paper.

• The concentric circles surrounding the wire's cross-section represent magnetic field lines.

• The rule to determine the direction of the magnetic field lines is called the right hand curl rule. In this rule, your thumb points in the direction of the current fingers curl in the direction of B

• The equation to calculate the strength of the magnetic field around a current-carrying wire is: B perpendicular = µoI / (2πr) where

– µo, permeability of free space = 4π x 10-7 Tm/A

– I, current flowing through the wire, measured in amps – B, magnetic field strength, measured in Tesla – r, distance from the wire, measured in meters

Ampere's law• Ampere's law allows the

calculation of magnetic fields.• Consider the circular path

around the current shown below. The path is divided into small elements of length (Δ l). Note the component of B that is parallel to Δ l and take the product of the two to be B∥Δ l. Ampere's law states that the sum of these products over the closed path equals the product of the current and μ: or

• For a long straight wire:

I

r

Bl

Magnetic Field near a coilWhen a current carrying conductor is formed into a loop or several loops to form a coil, a magnetic field develops that flows through the center of the loop or coil along its longitudinal axis and circles back around the outside of the loop or coil. The magnetic field circling each loop of wire combines with the fields from the other loops to produce a concentrated field down the center of the coil.

The strength of a coil's magnetic field increases not only with increasing current but also with each loop that is added to the coil. A long, straight coil of wire is called a solenoid and can be used to generate a nearly uniform magnetic field similar to that of a bar magnet.

Direction of Magnetic Field near a coilSecond right hand rule: Imagine holding an insulated coil with your right hand. Curl your fingers around the loops in the direction of the conventional current. Your thumb points toward the N-pole of the electromagnet.

Force on a current carrying wire• Moving charges experience a force in a magnetic field, so a current-carrying wire

will experience such a force, since a current consists of moving charges.• The interaction between the magnetic field of the wire and the external magnetic

field is exhibited by a force which is calculated with the formula: Fmax = BIL where B is the external, perpendicular magnetic field measured in Tesla, I is the current measured in amps, and L is the length of the current segment (in meters) that lies in the external magnetic field, B.

General Case: field at angle relative to current.

max sinF BIl

I

B

B sin

Force on a wire carrying current in a magnetic field

x x x xx x x x x

x x x x x xx x x x xx x x x

x x x xx x x x x

x x x x x xx x x x xx x x x

I = 0 I

Bin Binx x x x

x x x x x x x x x x x

x x x x xx x x x

I

Bin

Force on two current carrying wire• If two parallel wires have

currents traveling in the same direction, the magnetic fields generated by those currents between the wires will both point in opposite directions resulting in the wires attracting each other.

• if two parallel wires have currents traveling in opposite directions, the magnetic fields generated by those currents between the wires will both point in the same direction, in this case, into the plane of the page. These wires would repel each other.

Force from other (teal) wire is shown In red above

Force from other (blue) wire is shown In red below

Force on a single charged particle

+q

F

B

v

• Another right hand rule! This one provides a convenient trick to remember the spatial relationship between F, v, and B.

• If the moving charge is negative instead of positive, the direction of the force is opposite to that predicted by the right hand rule.

• The direction of the magnetic force is always at right angle to the plane formed by the velocity vector v and the magnetic field B.

F = qvBsin

B= F/qvsin

Right Hand Rule

Magnetic Fields – Direction and Magnitude• Direction of magnetic field at any point is defined as the direction of motion of a charged

particle on which the magnetic field would not exert a force. F = qvBsin– is the angle between the field and the velocity. If the angle is zero, sin is zero and there is no

force. The component of velocity of the charged particle that is parallel to the magnetic field is unaffected, i.e. the charge moves at a constant speed along the direction of the magnetic field.

• Magnitude of the B-vector is proportional to the force acting on the moving charge, magnitude of the moving charge, the magnitude of its velocity, and the angle between v and the B-field. B= F/qvsin

BvBv

+q

+q

Motion of Charged Particle in magnetic field• Consider positively charge particle

moving in a uniform magnetic field.• Suppose the initial velocity of the

particle is perpendicular to the direction of the field.

• Then a magnetic force will be exerted on the particle and make follow a circular path.

• The magnetic force produces a centripetal acceleration

• The particle travels on a circular trajectory with a radius:

• Magnetic forces do NOT do any work on moving charges since F and v are perpendicular.

Fv

q

r

Binmvr

qB

2mvF qvB

r

Thomson’s Experiments

• The discovery of the electron. Near the end of the nineteenth century scientists suspected that electrical phenomena were produced by tiny charged particles. J. J. Thomson (1856-1940) proved this fact with an experiment on cathode rays.

• He called these particles ELECTRONS and made the first step in determining their physical properties by measuring their charge-mass ratio (q/m). To do this, he built a special and completely evacuated tube like the one below:

• Thomson knew that electrons could be deflected by a magnetic field.

• And by balancing the magnetic and electric forces, kept the electron beam flowing along the original direction

• This relationship let him to compute the velocity of each electron through the ratio of the two balanced fields:

Thomson’s Experiments

• If the electric field is turned off, on the force due to the magnetic field remains.

• The magnetic force is perpendicular to the direction of motion and the electrons follow a circular path with radius R.

• The magnetic force is a centripetal force so

• Solving for q/m results in the charge to mass ratio for an electron:

• Thomson was also able to find the q/m for a positive ions and determine the mass of a proton.

Thomson’s Experiments

Electric Motor• An electric motor, is a machine which converts electrical

energy into mechanical (rotational or kinetic) energy.  

• A current is passed through a loop which is immersed in a magnetic field. A force exists on the top leg of the loop which pulls the loop out of the paper, while a force on the bottom leg of the loop pushes the loop into the paper

Electric Motor

The net effect of these forces is to rotate the loop.

• Imagine a current loop in a magnetic field as follows:

Electric Motor - Torque on a Current Loop

BI

b

a

B

a/2

F

F

F

F

1 2F F BIb

max 1 22 2 2 2a a a aF F BIb BIb

max BIba BIA sinBIA

Electric Motor - Torque on a Current Loop• In a motor, one has “N” loops of current is the angle between normal to the plane of the loop and the direction of

the magnetic field and A is the area of the “loop”

sinNBIA

Electric Motor

Brushes on the DC motor

To keep the torque on a DC motor from reversing every time the coil moves through the plane perpendicular to the magnetic field, a split-ring device called a commutator is used to reverse the current at that point. The electrical contacts to the rotating ring are called "brushes" since copper brush contacts were used in early motors.

Galvanometer• A galvanometer is an electromagnet that interacts with a

permanent magnet. The stronger the electric current passing through the electromagnet, the more is interacts with the permanent magnet.

Galvanometers are used as gauges in cars and many other applications.

The greater the current passing through the wires, the stronger the galvanometer interacts with the permanent magnet.

Northern Lights• The solar wind is constantly bombarding the Earth’s

magnetic field. Sometimes these charged particles penetrate that field. These particles are found in two large regions known as the Van Allen Belts.

• The Earth’s magnetic field extends far into space. It is called the “magnetosphere”. When the magnetic particles from the sun, called “solar wind”, strike this magnetosphere, we see a phenomenon called …..

Northern Lights

……Northern Lights.

Electric Field vs. Magnetic Field

Electric MagneticSource Charges Moving ChargesActs on Charges Moving ChargesForce F = Eq F = q v B sin()Direction Parallel E Perpendicular to v,B

Sources

• http://www.physics.wayne.edu/~apetrov/PHY2140/#lectures

• Physics by Zitzewitz• http://dev.physicslab.org/Document.aspx?

doctype=3&filename=Magnetism_CurrentCarryingWires.xml

• http://www.cliffsnotes.com/WileyCDA/CliffsReviewTopic/Electromagnetic-Forces-and-Fields.topicArticleId-10453,articleId-10435.html

• http://digilander.libero.it/mfinotes/VEuropeo/Physics/thomson.htm