ELECTROMAGNETISM introduction
IN CONSTRUCTION
references: THe physics of every day phenomena, A conceptual introduction to Physics - Mac Graw hill
Conceptual Physics, Paul Hewitt
http://physics503.one-school.net/
http://physics503.one-school.net/2008/06/what-is-electromagnetism.html
in construction, please be patient.
INTRODUCTION
1) In a previous chapter, we saw that a stationary charge produces an electric field in the space around. Likewise, a stationary
charge placed in an electric field will experience an electric force called the Coulomb's force.
The force is a vector along the electric field lines.
 In green the electric field lines generated by 1 positive charge. A test charge qo (small compared to the source) experiences an electric force. The direction is the same than the force field lines (electric field lines) |  SAme idea with a negative source instead. |
Likewise a moving charge can alter space and produce a magnetic field in every point of the space.
Also, a moving charge, in a magnetic field, will experience a magnetic force. (we will see that in a coming chapter)
However, the interaction between a moving charge and a magnetic field is more complex. The magnetic force is no longer along the field
but perpendicular to it. It is also perpendicular to the motion of the charge. And the charge does not speed up,
the acceleration is centripetal. (the magnetic field change the direction of the motion of the charge, it curves its trajectory)
but the magnetic field does not change the speed of a moving charge. (an electric field can accelerate a charge initially at rest or moving)
A uniform magnetic field B will act on moving charges
(for example inside a current-carrying wire) I .
The moving charges will experience a force magnetic
F. We will see some examples below.
Or You move a current-carrying wire with a force F
inside a magnetic field B and you produce an
electric current I (moving charge).
B, F and I (or moving charge(s) ) are perpendicular to
each other.
PART1: MAGNETIC FIELD OF MAGNETS
2) A magnet produces a magnetic field. This is because inside the magnet the electrons
play the role of moving charges. In most materials, the motion of electrons
is random and no net magnetic field is produced. In a magnet, some electrons
spins (around the nucleus and around themselves) and rotate the same way producing a net magnetic field.
 |  Magnetism originates in the motion of the electrons in iron. spinning electrons act like tiny magnets. Cancellation of this effect occurs in most materials. Iron,nickel, cobalt are exceptions. 2 motions are responsible for the total magnetic field. The rotation around the nucleus (major contribution) and rotation of the nucleus on itself. |
learn more here
3) You need only 1 single charge to produce an electric field. But a magnet has 2 poles.
A north pole and a South pole. If you break a magnet you get 2 magnets.
You can keep breaking it again and again till you reach the atomic scale. You won't be able
to isolate a pole. called a monopole. Although, some physicists are still trying to.
4)
A small compass will experience a force ( a torque) and will rotate where ever a magnetic field is.
The compass will align itself along the field lines.
You can use small magnet to map the space around a magnet to visualize the magnetic field.
The magnetic field comes out the North pole and comes in the South pole. See pictures below.
 2 opposite poles attract , the same way 2 opposite charges attract. Likewise, the force decreases with the distance squares. The force is inversely proportional to the distance squared. 2 like poles repel. |  small compasses can be used to map the magnetic field. You can also use iron filing trapped in a Plexiglas. Place the magnet on the Plexiglas. The iron filings behave like tiny compasses. | |
 In blue the magnetic field lines generated by a magnet. The pattern is similar to a electric dipole with 2 opposite charges. |  A magnet placed in a magnetic field will experience a torque and will aligned itself along the field lines. Like wise a dipole (made of 2 opposite charges of same magnitude) would too. | |
 The magnetic north-south axes of groups of iron atoms line up in the same direction. These groupings are called domains. In unmagnetized iron, the domains are randomly oriented. An external magnetic field will twist the domains into alignment |  If you cut a bar magnet in 2, you get 2 smaller magnets with their own magnetic fields. |  An electric current produces a magnetic field in the space around. The magnetic field can be mapped by a compass. We will get back to this phenomenon later. It proves magnetism and electricity are 2 aspects of the same theory. They are inter winded. |
5) magnetic field of the EArth
The Earth has its own magnetic field . Its magnetic field looks like the one produced by a bar magnet. (see above and below).
 The magnetic field of the earth is similar to the one of a bar magnet. Everything happens like there is a huge bar magnet inside the Earth. Interestingly The magnetic North is really the South pole of the " bar magnet " That's why it attracts the North pole of a compass. Note that a compass needle is just a small bar magnet. It was Sir William Gilbert, physician to Queen Elizabeth who suggested in 1600 that Earth was a giant magnet.  |  The geographic North does not exactly matches the magnetic North (see image above). Plus the magnetic North wanders around month after month . (it moves at a rate of 10 miles a year). It is currently somewhere off Wester Green land at about 77N102W.  |  Today, we think that the magnetic field is produced by the Earth's hot outer shell of molten iron sloshing around a solid inner core. As this subterranean ocean of liquid metal slowly whirls around, it behaves like a dynamo generating electrical currents and magnetic fields. |
 The Earth's magnetic field also stretches several hundred miles into space and protects us from the sun's charged particles and cosmic rays by focusing them towards the poles. This is where they appear as the northern and southern lights as they excite gases in the atmosphere.  As the magnetic poles migrate across the world, those night lights are going to light up some very strange places where they have never been seen before. Also, the magnetic poles of the Earth reverse (switch) every half-million years. (about). hat means the magnetic South will soon match the geographic North and vice versa!! We know that by observing natural magnets (iron bearing minerals like magnetite) frozen in solidified magma or sedimentary strata. half million years ago a compass was pointing South ! |
|
If the magnetic field disappear for a given amount of time, our cell phones or all our devices relying on electromagnetic waves will be disturbed. It will be a very messy time. Animals will be also affected. Birds and other animals like bees and bacteria have inside them natural compasses. (they have been found in the skulls of pigeons). These compasses help them to migrate or to orient themselves. They will be disturbed too. |
6)magnetic field of the Sun
Our sun too has a magnetic field but more complex. The Sun too rotates on itself like the Earth.
Because the rotational speed is significantly greater at the equator (27 days) than at the pole (37 days),
the pattern of the magnetic field is more complex . The pattern gives rise to loops of magnetic field line called prominences.
The bases of the loop are the black sunspots. They always occur in pairs.
 Here is a photo of one of these loops. Some charged materials (electrons and H+) are ejected from deep inside the Sun and are trapped in the loop (made of field lines). The loop is about 50,000km in diameter. ) The loop has 2 " feet" called sunspots. The charged material or ions move from one sunspots to the second one. These sports are cooler (2000K cooler) than other parts of the sun, that's why they appear black. |  | From the sunspots ions (charged particles), UV Xrays and gamma rays are ejected in space. These rays gives rise to the dangerous solar wind so dangerous for astronauts and life. Luckily, we have the magnetic field of the EArth to trap these rays. |
http://faculty.uncfsu.edu/aumantsev/active_sun.htm
PART2: MAGNETIC FIELD PRODUCED BY CURRENT in WIRES / COIL
INTRODUCTION ELECTROMAGNETISM -
1) Some history. Electromagnetism.
Until the lecture given by Oersted in 1819, magnetism and electricity were thought to be 2
well distinct phenomena. In a public lecture for the University of Copenhagen , Oersted
showed that an electric current can act at a distance on a compass.
The needle of the compass rotates until perpendicular to
the wire.
source: MacGrawHill
the Physics of every day phenomena.
He was the first one to demonstrate the connection between the 2 fields.
He already had in mind the unification of the laws of nature. So a moving charge
can produce a magnetic field. (the field lines called force lines
were only introduced later by Michael Faraday.)
Then comes Michael Faraday who showed that a magnetic field can
act , at a distance, on a moving charge. He understood that if an electric current
(moving charges) can create a magnetic field (like shown by Oestred) then a magnetic
field can produce a current (can move charges in a conductor). He believed that natural
phenomena demonstrate symmetry. He introduced the lines of forces later called electric field.
Michael Faraday has an amazing story. He was the son of a blacksmith and he made his way
to the Royal institution of London. See Giants.html.
Then comes James Maxwell we studied Faraday's discovery and developed
the mathematical formulation for electromagnetism. The formulation is
the same used to describe the behavior of fluids. An electric field
flows like water. A magnetic field spins like a vortex. (see giants.html for details)
2) A wire of current produces a magnetic field. You can visualize the magnetic field using small
magnets or using iron fillings.
 in the lab. Iron filling experience a torque and align along the field. |  unlike an electric field, a magnetic field has no starting point. A magnetic field spins live a vortex around the source. |  use your right hand to find which way the field spins. Thumb up, wrap the hand around the circuit such has the thumb shows the direction of the current. |
Nice applet to understand better
3) What about the magnetic field produced by a coil (a loop or more of current-carrying wire ? )
We get an electromagnet with a North and a South pole.
 Take a wire and its magnetic field and make a loop. you can then understand the pattern of the magnetic field this way. |  magnetic field created by a loop of current. The loop has a North Pole and a South pole. wrap your right hand around the loop such your fingers follow the senses of the current. Your thumb points to the North. The lines come out of the North face and in the South face. |  How to find the North Pole of a loop or more of current. This is called the right hand rule. The thumb points to North. |
3) The magnetic field produced by a straight wire is non uniform. The magnitude of B is inversely proportional
to the distance from the wire and its direction is non uniform. (the vectors B are not parallel).
Let's look at magnetic field that can be considered as uniform:
- The magnetic field inside a horseshoe magnet is uniform. (between the 2 legs)
- The magnetic field produced inside a solenoid is uniform.
A solenoid is a coil made of loops of current-carrying wire. Its length has be great compared to
its diameter. The magnetic field produced is very much like the one produced by a bar magnet.
The North and South pole is found using the right-hand rule. You can make the
magnetic filed stronger by inserting an iron rod inside. you get an electromagnet.
 source: excellent Physics website  |  magnetic field produced by a solenoid. It is almost uniform inside. B = uo N I / L uo is a magnetic constant = 4 pi 10-7 N is the number of loops I is the current, L is the length of the coil So B is constant. N/L is the number of loops per unit length. (R is the radius and is small compared to L, R << L ) source: The Physics of every day phenomena, Mac GRaw Hill |
- The magnetic field produced by the Helmholtz coils is also uniform. This system is made of 2 loops
of wires placed at a distance R form each other. The distance between the coils = radius of the coils.
 The magnetic field is uniform between the coils. B = 0.72 uo NI / L with L = R the radius. N/+L is the number` of loops per length. uo= 4 pi 10-7 N /A2 |  |
check animations to visualize fields
PART3: PROBLEMS WITH MAGNETIC FIELDS
1) a Lodestone is a natural ______________. If a steel pin is stroked in one direction with the
________, the pin will become __________ as well.
2) 2 bar magnets are placed perpendicular to each other as shown below. Their field are B1 = 2 10-3 Telsa
dand B2 = 3 10-3 T . draw the vectors B1 and B2 as well as the total field B = B1 + B2 (adding vectors).
Find the magnitude of B.
3) 3 bar magnets are placed as shown below. Trace the total magnetic field D at O. B = B1 + B2 + B3.
You need to find the direction of B (angle with horizontal) and magnitude. On a graph paper
add the vectors. 1 square = 10-3 T, it will help you to find the angle and the magnitude,
B1= 2 10-3 T B2 = 3 10-3 T B3= 4 10-3 T
4) 2 Helmotz coils have a diameter of 20cm. They have each 14 loops. The current I is I = 500mA.
A) How far the coils must be to be able to use the formula : B = 0.72 uo NI / L uo= 4 pi 10-7 N /A2
B) Find the magnetic field between the coils.
5) A current I = 2A is flowing in Helmholtz coils. The radius is 10cm.
Find the magnitude of B
6) You want to build a 50cm long solenoid that will produce a magnetic field = 2 mT.
The current is 1A. How many loops you need ? (find N) B = uo N I / L
7) a compass is placed inside a solenoid as shown below. Observe the compass and derive the direction of the current.
8)Observe the following coils. Are they attracting each other or repulsing each other?
9) the field in the center of a flat coil is give by the formula: B= B = uo N I / 2R uo= 4 pi 10-7 N /A2
where R is the radius of the coil and I the current in the coil. If B = 2 10-4 T, N= 10 loops and R = 15cm
Find the current I that flows in the loops.
10) What kind of relationship is there between the field produced by the Helmotz coils and the diameter of the coils ?
If the radius increases, the magnetic field __________- So why the coils have usually large radius ?
(hint; Radius = distance between coils for the Helmotz set up)
11) Consider a solenoid without any current. If a compass (see picture) is placed inside the solenoid, the compass shows the
horizontal component of the magnetic field of the EArth BT (vector) Find the value of the current you need so the
compass rotates by 30 degree celcius BT = 2 10-5T. The number of loops per unit meter is 2000 loops per meter.
use the formula B = uo N I / L with N/L = number of loops per unit length (2000)
12) What are the 3 set up that will produce an uniform magnetic field. Write the formula that gives B if you know it.
13)
The field lines of a solenoid are shown using iron filling.
A) Using the direction of the current, find the North side and the South side of the solenoid. SHow the direction
of the field along the lines.
B) Using a telsameter the magnitude of the field B(x) inside of the solenoid as a function of the distance x from the center
of the solenoid 0 are recorded, A graph magnitude B vs distance x is made (see picture below)
IS the graph consistent with the pattern of the field lines (A) ?
C) For which length of the solenoid the value of the field is less than 10% smaller than the value Bo for x=0.
(is no smaller than 10% of Bo).
D) Find the current I that flows in the solenoid for L = 40.5 cm and N = 500 loops.
E) some students are now studying how the magnetic field varies when the number of loops varies.
(B versus N). B is the __________ variable, N is the _________ variable . L and I
stay constant. THey are the ____________ variables.
The data are recorded below. (they have several solenoid of different length)
| solenoid | S1 | S2 | S3 | S4 | S5 |
| N | 400 loops | 600 | 700 loops | 800 | 1000 loops |
| Bo(mT) | 2.50 | 3.78 | 4.40 | 5.00 | 6.30 |
F) Graph Bo versus N (number of loops). Lab the axis, give a title, watch the units.
Find the equation of the line. Bo = ____________. What kind of relationship is there between Bo and N.
G) Is the slope consistent with the formula B = uo N I / L or Bo = uo I/L N ?
(compare the slope with uo I/L) . Remember Bo is in millitelsa.
H) We now consider the solenoid S1 with N = 400 loops. (see table). When no current circulate, a compass shows the direction
of the horizontal component of the magnetic field of the Earth and make an angle of 20 degrees with the axis of the solenoid.
When the current is turned on, the needle moves by a SMALL ANGLE . Find the new angle the needle makes with the axis of the solenoid.
BT = 2 10-5T (horizontal component of the magnetic field of Earth) and I = 20mA
PART 4: INTERACTION BETWEEN CURRENT-CARRYING WIRES / COILS
2 current-carrying wires or loop can interact with each other through
their magnetic fields. Here some examples:
1) 2 vertical current-carrying wires can attract or repel with a force F
 2 wires with currents flowing in the same direction will undergo attractive magnetic forces. If the currents run in opposite direction, the forces repel. HERE is the demonstration | REmember that a current-carrying wire produces a magnetic field such as the vectors B (at a given point in space) are perpendicular to the direction of motion of the charges that is perpendicular to I, the flowing current. |
APPLET
2) 2 coils or 2 solenoids can behave like 2 magnets. The alike poles repel and the opposite poles attract.
The poles are given by the right hand rule.
 Like for the vertical wires, these 2 loops attract each other. The current is flowing in the same direction. The North face of the above loop attracts the South face of the below face. |  same idea. the solenoids behave like 2 bar magnet. The can repel or repel depending on the sens of the current. |
3) The coil below is approached by a magnet as shown below. Is there attraction or repulsion?
PART 5 : SOME APPLICATIONS OF ELECTROMAGNETISM AND ELECTROMAGNETS
The magnetic field is proportional to the current and to the number of loops.
electromagnets can be used to:
lift car or heavy metal objects.
 lifting electromagnet are used to lift very heavy object in a factory. |  |  electromagnet can be use to separate metal from other material to recycle. This is called an electromagnet separator. |
2) GENERATOR B+F = I
 GENERATOR Again a coil is used to build a generator of electricity. The coil turns at a constant rate in an uniform field. Like the one generated between the 2 legs of the horseshoe magnet. Observe the snapshot above. You have a magnetic field along the X axis and a force along the Z axis. (the torque that moves the loop). So the charge will move along the Y axis in the wire. You are generating a current. This was found by Michael Faraday. (electromagnetic induction) |  This concept explains how to make electricity. You can use steam to spin a turbine that spins the coils in an uniform magnetic field to generate electricity. Steam can be produced by burning fossil fuel (coil, oil), by using the energy released by nuclear fission (nuclear plant) . You can also use the wind or water to turn the coil. (natural resources). |
3) motor B+I=F
 Same idea for the motor. Here a direct current moves along theY axis (see previously) inside a magnetic field B along the X axis so a force F is produced along the Z axis. A torque that will rotate the loop. See here how moving charges (I) + B can produce a force |  Same idea. I + B = F |
4) This principle (I + B + F) is used in many electric systems.
Like the loudspeaker or microphone
 The current flows back and forth in the wires inside a magnetic field. This will move a paper cone at the same frequency back and forth. The cone generates sound waves at the same frequency. Sound is created. so I + B = F |  A microphone works the other around. Sound waves moves back and forth a coil inside a magnetic field (produced by a bar magnet) This will generate a current. F + B = I |
5) other applications for electromagnets
 electric bell use an electromagnet It used electricity and s solenoid. the iron rod inside the coil magnifies the magnetic field. When you push the switch. you close the circuit and the current flows. the coil becomes an electromagnet that attract an iron striker that hits the bell. It open the circuit so the striker moves back. and so forth. source: learn more about EM applications | |
 electric relay. A small 1 circuit relies on a small current. When it is switched on the electromagnet attracts the iron arm that close the circuit2 that usually can stand larger current. This system is used in the starter system of the car. to learn more, excellent website about EM applications |  works like a fuse. When the current is too large, the magnet is strong enough too open the circuit. The magnetic field is proportional to the current. source: learn more about EM applications |
Here for more applications
6) here are more applications
 the principle I + B = F can be used to measure the current or the voltage in an electric circuit. A coil is placed in a constant magnetic field B. When the current I flows in the coil, a magnetic force F(perpendicular to I and B) moves the needle held by a spring. The amount of deviation is proportional to the current I. The scale can be in volts or amperes. |  A cyclotron was the first accelerator of charged particles like protons or electrons. A constant magnetic field is used to act on the moving charged particle. The force perpendicular to the motion of the particle makes it turn but does not make it accelerate. We will see that later but you may remember how planets orbit the Sun. The gravitational force make them spins but does not accelerate them. Once the particle is done with half a circle an electric field accelerate the particle in the gap. The speed is changed and so is the curvature when the particle is back in the magnetic field. |  source: best Physics website http://hyperphysics.phy-astr.gsu.edu/HBASE/magnetic/cyclot.html#c1 |
7) other application : hall probe used to measure the magnetic field , for example in a solenoid.
The unit is Telsa. It is based on the probe effect.
 probe to measure the magnetic field in a solenoid. |  Hall effect. Consider this flat conductor. (part of the probe). A current I flows in a constant (uniform) magnetic field B. The moving charges experience a transverse force ( I + B = F). some charge will build up on the sides producing a voltage Vh. This voltage is proportional to the field B giving a way to measure B. |
8) mass spectrometer and velocity selector.
 This device is used to classify atoms according to their mass. This classification can be used to identify them. In a space ship the device can identify ions making up the cosmic rays. In a first step the atoms are ionized (electrons are removed) then the ions are accelerated using an electric field (we will see that later). The ions enter a uniform magnetic field region. The moving charge will experience a force F perpendicular to their motion and that will result in a circular motion. The radius of the motion depends on the mass (inertia) of the charge. |  velocity selector. Used to select particles (same mass and charge but different speed) that have a given speed. The charged particles experience 2 forces along the vertical. An electric force and a magnetic force. When these 2 forces (for a given speed ) balance each other, the particles are not deflected and can be selected. |
9) Magnetic field can be used in other high technology set up like the Nuclear Magnetic Resonance spectroscopy
that allow scientists to probe the soft tissues of the human body. It can also be used to probe the atomic structure
of crystals. A uniform magnetic field is used.
Also, when scientists want to store plasma (very very hot ionized particles), they can't use containers
that can't take the high temperature. they can use the magnetic field to guide and trap the
particles. They can use plasma to try fusion (like in the sun) to produce clean energy (clean electricity).
They can also produce voltages.
PART IV problems coming soon
try the problems here
more problems