Lecture Notes (Magnets: Permanent & Temporary)

Intro: - today we will begin discussions on magnetism; we will start out with some historical notes and then make our way to properties of magnets History of Magnets: - the phenomenon of magnetism has been known for thousands of years; lodestone (a magnetized form of the commonly occurring iron oxide mineral magnetite) was the first permanent magnetic material to be identified and studied - the ancient Greeks were aware of the ability of lodestone to attract small pieces of iron; the Greek word magnes, which is the root of the English word magnet, is thought to be derived from Magnesia, the name of a region of Greece where lodestones were commonly found

Lodestone

- the magnetic compass was invented some time during the first ten centuries AD; credit is variously given to the Chinese, the Arabs, and the Italians

- what is certain is that by the 12th century magnetic compasses were in regular use by mariners to aid navigation at sea - in the 13th century, Peter Perigrinus of France discovered that the magnetic effect of a spherical lodestone is strongest at two oppositely directed points on the surface of the sphere, which he termed the poles of the magnet - he found that there are two types of poles, and that like poles repel one another whereas unlike poles attract - in 1600, William Gilbert hypothesized, that the reason magnets like to align themselves in a north-south direction is that the Earth itself is a magnet (Gilbert was also physician to Queen Elizabeth I) - Gilbert added that the Earth's magnetic poles are aligned, more or less, along its axis of rotation - the geographic North Pole of Earth corresponds to a magnetic south pole, and the geographic South Pole of Earth corresponds to a magnetic north pole

Compass

William Gilbert (1544 -1603)

- in 1820 Hans Christian Ørsted (Danish physicist) was giving a lecture demonstration of various electrical and magnetic effects - suddenly, much to his surprise, he noticed that the needle of a compass he was holding was deflected when he moved it close to a current carrying wire - this was a very surprising observation, since, until that moment, electricity and magnetism had been thought of as two distinct phenomena - word of this discovery spread quickly along the scientific grapevine, and the French physicist Andre Marie Ampère immediately decided to investigate further - Ampère's apparatus consisted (essentially) of a long straight wire carrying an electric current

Ørsted (1777-1851)

- Ampère quickly discovered that the needle of a small compass maps out a series of concentric circular loops in the plane perpendicular to a current carrying wire

- the direction of circulation around these magnetic loops is conventionally taken to be the direction in which the north pole of the compass needle points - one easy way to remember that a straight current carrying wire produces circular lines of magnetic force is to use the first right hand rule - if the thumb of the right-hand points along the direction of the current then the fingers of the right-hand circulate in the same direction as the magnetic loops

Magnetism Basics: - magnetic fields are established in two ways: 1. Permanent magnetic materials Ex. ALNICO V 2. Electromagnets (the field set up by moving charges or currents)

- temporary magnets can be created Ex. nails, paper clips, iron filings, etc... when influenced by a permanent magnet or electromagnet

- we say that magnetism is induced in the paper clip, nail, etc... - the temporary magnets will become polarized (having a north and south pole) and will act as magnets themselves; if you remove the permanent magnet or electromagnet, the temporary magnet will cease functioning Permanent Magnets: - only iron and a few other materials such as cobalt, nickel, and gadolinium show strong magnetic effects; these four metals are said to be ferromagnetic (from Latin word “ferrum” meaning iron). - contrary to popular belief, most metals have very little magnetism - other metals show some slight magnetic effect, but it is extremely small and very difficult to measure - permanent magnets are created in the same way as temporary magnets, except the atomic structure is such that the magnetic properties will be retained - some materials, such as ALNICO (aluminum, nickel, and cobalt), and neodymium and gadolinium produce extremely strong permanent magnets for their size

NdFeB permanent magnets are mainly made of Neodymium, Iron and Boron.   NdFeB magnets can be used as an ideal magnet in mini‐motors and hard drives. 

Magnetic Field Lines: - magnets apply forces over long distances, like gravity and electrostatic forces, they are not contact forces - these long range forces can be described by the concept of fields - every magnet forms magnetic fields around it; the presence of these fields can be visualized by iron filings

- remember that while magnetic fields exist in reality, magnetic field lines do not exist in reality, they are merely a construct we use to understand magnetism

- the number of magnetic field lines passing through a surface is called the magnetic flux - the flux per unit area is proportional to the strength of the magnetic field; in magnets the magnetic flux is concentrated at the poles - the direction of a magnetic field line is defined as the direction in which the N-pole of a compass points when it is placed in the magnetic field - the field lines exit the magnet at its N-pole and enter at the magnets S-pole; the field lines form closed loops

- magnetic fields apply forces on other magnets; the N-pole of one magnet repels the N-pole of another magnet in the direction of the field line

- conversely, the N-pole of one magnet attracts the S-pole of another magnet in the direction of the field line

Electromagnetism: - as mentioned earlier, Hans Ørsted (Danish) discovered in 1819 that a current (i.e. moving charges) flowing in a wire produces a magnetic field around the wire - he visualized this by seeing a compass needle deflect as he brought it near the wire

- another way to visualize this phenomenon would be to place the wire through cardboard and place iron filings around the wire; the filings will form a pattern of concentric circles around the wire

- a charged particle, stationary or moving, creates an electric field; a moving charge creates a magnetic field - the motion is relative: 1) a moving charge creates a field 2) you moving relative to a fixed charge also creates a magnetic field - right hand rule for a straight current carrying wire: take the wire in your right hand so that it lies across your palm, ⊥ to the outstretched fingers, the extended thumb gives the current direction; curl your fingers around the wire; the direction of curl gives the direction of the magnetic field lines Magnetic Fields Near Coils: - if a wire carrying electric current is made in a loop, it will form a magnetic field all around the loop

- you can apply the first right hand rule at any point of the loop to find the direction of the magnetic field - if you loop the current carrying wire many times you form a solenoid

- as you can see in the figure above, the solenoid has a magnetic field around the loops in only one direction - the magnetic field from each loops of the wire reinforces each other to form a strong field - the solenoid has a field like that of a permanent magnet; it has a N-pole and a S-pole - a solenoid's magnetic field strength will increase if you:

1) increase the current in the wire 2) increase the number of coils in the wire 3) place an iron rod or core inside the coil

- the direction of the magnetic field of a solenoid can be found by using the second right hand rule; when you coil your fingers around the wire loops in the direction of the current, your thumb will point to the N-pole of the electromagnet

Microscopic Picture of Magnetism: - from atomic theory it is known that an atom is made up of a nucleus of protons surrounded by one or more electrons encircling it - the rotation of electrons and protons in most atoms is such that the magnetic forces cancel each other - atoms or molecules of the elements iron, nickel, and cobalt arrange themselves into magnetic entities called domains; each domain is a complete miniature magnet - groups of domains form crystals of the magnetic material; the crystals may or may not be magnetic, depending on the arrangement of the domains in them - investigation shows that while any single domain is fully magnetized, the external resultant of all the domains in a crystal may be a neutral field

- substances that can be made to form domains are said to be ferromagnetic, which means "iron magnetic"; the ferromagnetic elements are iron, nickel, and cobalt - it is possible to combine some non-magnetic elements and form a ferromagnetic substance; for example, in the proper proportions, copper, manganese, and aluminum, each by itself being non-magnetic, produce an alloy which is similar to iron magnetically

Lecture Notes (Forces Caused By Magnetic Fields)

Intro: - as you saw in studying Coulomb’s law, electrically charged bodies exert forces on each other; when the charged bodies are at rest, the forces are “electric” forces, or Coulomb forces - “electric fields” act as the sources of these forces; but when the charged bodies are moving (as when two parallel wires carry currents), new forces in addition to the electric forces are present - these new forces are called “magnetic” and are caused by “magnetic fields” set up by the moving charges Forces on Currents in Magnetic Fields: - experiments show that a stationary charged particle does not interact with a static magnetic field, however, when moving through a magnetic field, a charged particle experiences a magnetic force - this force has a maximum value when the charged particle is traveling in a direction perpendicular to the magnetic field - the magnetic force has a minimum value when the charged particle is traveling along the magnetic field lines - there is a helpful rule that relates the velocity (v) of the charged particle, the direction of the magnetic field (B), and the magnetic force (F) experienced by the charged particle; it is called the third right hand rule

- the third right hand rule states that with your thumb in the direction of v and your four fingers in the direction of B, the force is directed out of the palm of your hand

- the mathematical relationship of magnetic force can be summarized as follows:

sinθqF vB

- magnetic force, F, is in newtons (N) - electric charge, q, is in coulombs (C) - velocity of the charged particle, v, is in meters per second (m/s) - magnetic field strength, B, is in teslas (T) - angle theta, θ, is the angle between the direction of v and the direction of B is in degrees (°) - many times another unit is substituted for magnetic field strength B; instead of teslas another unit called the gauss (G) is used - the conversion for these units is: 1 T =104 G - as stated earlier the magnetic force is maximal when the charge is traveling perpendicular to the field (θ = 90°)

- the force is minimal (zero) when the charge is traveling along the field lines (θ = 0°) - the force on a wire in a magnetic field can be demonstrated using the experiment below:

- arrows are used to describe the direction of a magnetic field; when the direction of the field is into the page X's are used, when the field is coming out of the page dots are used

X X X X X X X X X

· · ·

· · ·

· · ·

Magnetic field directed out of the page

Magnetic field directed into the page

- Michael Faraday discovered that the magnetic force on a current carrying wire is at right angles to both the direction of the velocity of the charge and the direction of the magnetic field (the experiment diagrammed in the pictures above) - up to this point we have been dealing with the magnetic force applied to a current carrying wire; let's take a look at the forces between wires carrying current

- as we can see in the diagram above, two current carrying wires will attract each other when the currents are in the same direction - conversely, two current carrying wires will repel each other when their currents move in opposite directions - it is possible to mathematically calculate the force of magnetism that is exerted on a current carrying wire passing through a magnetic field at right angles to the wire

- the equation is:

ILF B

- magnetic force, F, in newtons (N) - magnetic field strength, B, in teslas (T) - current in wire, I, in amperes (A) - length of wire, L, in meters (m) Loudspeakers: - a loudspeaker is one application of the force generated on a current carrying wire in a magnetic field - a loudspeaker converts electrical energy to sound energy using a coil of fine wire mounted on a paper cone and placed in a magnetic field

- the current in the speaker will change direction rapidly, causing the paper cone to vibrate; this is what generates the sound waves Galvanometers: - galvanometers are devices used to measure small amounts of electrical current

- galvanometers work by using the magnetic forces generated on a small piece of wire which is carrying a current - the magnetic forces create a rotational force (torque) on the wire; the greater the torque, the greater the current measured by the galvanometer

- these devices can read currents as little as 50 μA Electric Motors: - if you modify the design of a galvanometer slightly, you end up with an electric motor; the main difference between the two is that the current is made to change direction every time the coil makes a half rotation (180 º) - electric motors are designed this way so they can rotate a full turn of 360 º - an electric motors convert electrical energy to kinetic energy; they consist of a rigid current carrying loop that rotates when placed in the field of a magnet

- at this point (when the wire is in the same direction as the magnetic field lines) the force on the wire is zero - in an electric motor the loop has to be able to rotate a full 360º; therefore, the current must reverse direction just as the loop reaches 180º; this will allow the motor to provide continuous rotation in one direction

- split-ring commutators are used to reverse current direction - pieces of graphite that make contact with the commutators called brushes allow current to flow into the loop; graphite is used because it is a good conductor as well as a good lubricant - as the loop changes brushes, the current the loop experiences reverses and the loop continues to rotate - this process repeats every half-turn, causing the loop to spin in the magnetic field Electric Motor Animation - the loops of wire in an electric motor is called the armature; it is mounted on a shaft or axle - the total force acting on the armature is: n ILF B where n is the total number of turns in the armature

- the magnetic field is generated by permanent magnets or an electromagnet called a field coil; the speed of the motor is controlled by varying the amount of current through the motor Force on a Single Charged Particle: - charged particles do not have to be in a wire, but can also move freely through space - there are many applications for controlling the direction of a charged particle, but air must not be present, however, in order to remove any collisions with air molecules - televisions and computer monitors are examples of modern day cathode-ray tubes - a cathode-ray tube is a glass tube with a sealed wire at each end, each wire ended in a metal plate called an electrode; outside the tube, each wire runs to a source of high voltage (battery) - the negative plate is called the cathode and the positive plate is called the anode

Cathode ray tube

electrodes

anode cathode

ammeter

voltage source

- British physicist, J.J. Thomson (1856 - 1940) created the cathode-ray tube

- scientists discovered that if you pass an electric current through the low-pressure gas in the tube, the tube itself glowed with a pale green color

- it was shown that the green glow was produced by something that comes out of the cathode and travels down the tube until it hits the glass; hence the name cathode rays - in 1897, Thomson hypothesized that cathode rays were negatively charged particles; these were later called electrons - the electrons in a television or computer monitor are focused by magnets to form a narrow beam that move up and down the screen of the tube; the tube is coated with phosphor that glows when hit by an electron, thereby producing the picture

- the magnetic force on a single electron moving perpendicular to a magnetic field of strength B can be determined by the following mathematical equation:

qF B v - the charge is measured in coulombs, the velocity in meters per second (m/s) and the magnetic field strength in teslas (T) - note that when using the third right hand rule on finding the direction of the magnetic force on the electron, since it is negative you will have to use your left hand Auroras (Northern & Southern Lights): - when cosmic radiation, charged particles from the sun and other celestial phenomena outside our solar system, collides and interacts with molecules in our atmosphere, bright lights result

- these auroras occur only at locations near the north and south poles; they form here because of the structure of the Earth's magnetic field

- another interesting result of the structure of the Earth's magnetic field is the formation of two radiation belts around the planet - these belts are called the Van Allen belts named for their discoverer, James Van Allen - the Van Allen belts are composed of high- energy electrons and protons temporarily trapped in the Earth's magnetic fields

- any spacecrafts and/or persons traveling through these belts must have protective shielding to withstand the intense radiation

James Van Allen (1914-present)