Magnetism

1. Magnetism And Electromagnetic Induction

3. Warm-up • An electric dipole is made up of a positive and a negative charge with the field lines coming out from the positive and into the negative. • It is also possible to have a single positive or negative charge. • A magnet has two poles, North and South, with the field lines coming out from the North and into the South. • Is it possible just to have a North or a South?

4. No Monopoles Allowed • It has not been shown to be possible to end up with a single North pole or a single South pole, which is a monopole ("mono" means one or single, thus one pole). • Magnets always have both north and south poles. The reason why monopole magnets don’t exist is because the north and south poles are created by the alignment of the molecules inside. They are all aligned in the direction of the north pole, so even if a magnet is broken in half, the alignment of the molecules has not changed, so the north and south poles still exist. • Note: Some theorists believe that magnetic monopoles may have been made in the early Universe. So far, none have been detected. S N

5. History #1 • Term comes from the ancient Greek city of Magnesia, at which many natural magnets were found. We now refer to these natural magnets as lodestones (also spelled loadstone; lode means to lead or to attract) which contain magnetite, a natural magnetic material Fe3O4. • Pliny the Elder (23-79 AD Roman) wrote of a hill near the river Indus that was made entirely of a stone that attracted iron. • Chinese as early as 121 AD knew that an iron rod which had been brought near one of these natural magnets would acquire and retain the magnetic property…and that such a rod when suspended from a string would align itself in a north-south direction. • This ability of the lodestone allowed for the creation of compasses two thousand years ago, which was the first known use of the magnet. • Use of magnets to aid in navigation can be traced back to at least the eleventh century.

6. History #2 • In 1263, Pierre de Maricourt mapped the magnetic field of a lodestone with a compass. He discovered that a magnet had two magnetic poles North and South poles. • In the 1600's William Gilbert concluded that the earth itself is a giant magnet. Basically, we knew the phenomenon existed and we learned useful applications for it. We did not understand it. • 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!

7. Finally, the Science • In around 1830 Michael Faraday and Joseph Henry discovered that a changing magnetic field produced a current in a coil of wire. • 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. • Joseph Henry (first Director of the Smithsonian Institution) failed to publish what he had discovered 6-12 months before Faraday • In the 1960's and 1970's scientists developed superconducting materials. Superconductors are materials that have an extremely low resistance to a current flowing through them, usually at a very low temperature.

8. The Connection is Made Summary: Oersted showed that magnetic effects could be produced by moving electrical charges; Faraday and Henry showed that electric currents could be produced by moving magnets So.... Results: All magnetic phenomena result from forces between electric charges in motion.

9. Looking in More Detail • Ampere first suggested in 1820 that magnetic properties of matter were due to tiny atomic currents • All atoms exhibit magnetic effects • Medium in which charges are moving has profound effects on observed magnetic forces (we will mostly assume the medium is empty space, which is a reasonable approximation of air in this context).

10. Magnets and Magnetism • Magnetism is the force of attraction or repulsion of a magnetic material due to the arrangement of its atoms, particularly its electrons. • A bar magnet is made using these properties of electrons and atoms. If all of the magnetic poles due to these properties are lined up in a solid, a magnet is formed. • To make a magnet out of a metal, one can melt it, and expose it to a magnetic field as it becomes a solid again, causing the poles to line up and form a permanent magnet. • The region where the magnetic forces act is called the “magnetic field.”

11. Magnetic Fields • A magnet can be compared to a electric dipole, with field lines exiting one side and coming back into the opposite side. All magnets have a north end and a south end, field lines exit from the north and enter the south. • The difference between an electric field and a magnetic field, is that while an electric field effects all charges, a magnetic field only effects charges when they are in motion. • It was Michael Faraday who realized that a magnet has a ‘magnetic field’ distributed throughout the surrounding space. Electric field lines around a dipole Magnetic field lines of a bar magnet

12. Quantum Mechanics Explanation of Magnetism • Magnetic fields are due to the flow of electrons, also called an electrical current. This is how one can explain the intrinsic magnetic properties of electrons called spin angular momentum and orbital angular momentum. • Spin angular momentum - to understand this, you must understand that electrons have a property called spin, which is kind of conceptually analogous to the spin of a spinning top. This gives it spin angular momentum. Basically, along with orbital angular momentum, spin angular momentum gives it a vector quantity, meaning it moves with direction. • Here is a site that shows in a more complex way how the direction of the spin would affect the magnetic field.:Spin and Win • Orbital angular momentum just as it sounds; an electron orbits the nucleus of an atom and from this it carries orbital angular momentum. Conceptually you can think about it this way but this is not actually what happens. What actually occurs is very complicated and can only be explained with quantum mechanics.

13. Magnets Have Magnetic Fields We will say that a moving charge sets up in the space around it a magnetic field, and it is the magnetic field which exerts a force on any other charge moving through it. Magnetic fields are vector quantities….that is, they have a magnitude and a direction!

14. Force Due to Magnetic Field • As previously stated, the difference between an electric and a magnetic field is that where electric fields apply a force on any charged particle, a magnetic field only applies a force on a charge in motion. • The force felt by the charge in motion is given by the formula: F = q v B sin  F = Force (N) q = Charge on the particle (C) v = Velocity of the particle (m/s) B = Magnetic field magnitude (tesla - T)  = Angle between the velocity vector and the magnetic field

15. Effects of a Magnetic Field Remember: F = q v B sin θ When the charged particle is moving parallel to the magnetic field, the force on it is zero. No net force  q F But when the particle is moving in any other direction, there is a net force on the particle.

16. Force on Current Carrying Wire • The force exerted by the magnetic field on a current carrying wire is given by the formula: F = ILB F = Force (N) I = Current (A) L = The length of the conductor (wire) (m) B = The strength of the magnetic field (T)

17. Induced EMF (Voltage) • The electromotive force (EMF) induced in a wire moving through a magnetic field is given by the formula: EMF = B L v sin θ EMF = Electromotive Force (voltage) L = The length of the conductor (wire) B = The strength of the magnetic field v = velocity of the wire  = Angle between the velocity vector and the magnetic field

18. Equations I = q/t q = It units: C = As W = Fd units: J = Nm P = W/t = IV Units: W = J/s = AV F = ILB B = F/IL units: T = N/Am EMF = B L v sin θ units: (N/Am)(m)(m/s) = Nm/As = J/C = V

19. Equations F = ILB B = F/IL EMF = B L v sin θ F = q v B sin 

20. Earth’s Poles • The magnetic field of Earth is similar to that of a bar magnet. • The magnetic poles are not aligned with the rotation (geographic) poles of Earth. • The location of the magnetic poles changes with time and even flips with respect to the rotation poles over geologic history. • In the current era, the magnetic pole in the northern hemisphere is a south magnetic pole, which is why the north pole of compass needles point in that direction. Image Credit: UC Berkeley

21. Right Hand Rule #1 • Current moving in a wire creates a magnetic field. • Thumb points direction of current. • Fingers curl in direction of magnetic field

22. Right Hand Rule #2 • To find North pole of an Electromagnet: • wrap fingers around coil in direction of current flow • Thumb point to the North pole

23. Right Hand Rule #3 • Charge moving through a magnetic field: • B = fingers (palm to fingertips) show magnetic field lines (N to S) • v = thumb points in direction of the velocity of the charge • F = force is directed outward from the palm Magnetic field (B) for this picture = fingers into page; thumb points north (the original velocity of the charge); F is out from the palm.

24. Right Hand Rule #4 • Wire sitting in a magnetic field: • B = fingers (palm to fingertips) show magnetic field lines (N to S) • I = thumb points in direction of the current • F = force is directed outward from the palm I

25. Right Hand Rule #5 • Conductor (wire) not hooked to power source is moved through a magnetic field which creates an EMF (voltage and current): • B = fingers (palm to fingertips) show magnetic field lines (N to S) • v = thumb points in direction the wire is moved in the field • F = EMF (voltage) and corresponding current is directed outward from the palm

26. Units Used in Magnetism • ampere (A): The ampere is the SI base unit of electrical currents. • One ampere is the current that would create, between two infinitely long parallel wires with negligible cross section placed one meter apart in a perfect vacuum, a force of 0.2 micronewtons between each other per meter of length. • All other electrical units are all defined in terms of the ampere. • The unit is known informally as the amp, but A is its official symbol. • coulomb (C) The SI unit of electric charge. • One coulomb is the amount of charge accumulates in one second by a current of one ampere. • Since electricity a flow of electrons, one coulomb represents the charge of approximately 6.241 506 x 1018 electrons. C = s·A • tesla (T): The tesla is the SI unit of flux density (or field intensity) for magnetic fields. • A tesla is the field intensity required to generate one newton of force per ampere of current per meter of conductor. • A magnetic field of one tesla is very powerful magnetic field. Sometimes it may be convenient to use the gauss, which is equal to 1/10,000 of a tesla. • The tesla is probably the most important unit used in magnetism. T = N/A·m = kg/(A·s2)·m

27. For Every North, There is a South • The ends of a magnet are where the magnetic effect is the strongest. These are called “poles.” Each magnet has 2 poles – 1 north, 1 south. • Poles of a magnet always come in pairs. By convention, we say that the magnetic field lines leave the North end of a magnet and enter the South end of a magnet.  • 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

28. No Monopoles Allowed • It has not been shown to be possible to end up with a single North pole or a single South pole, which is a monopole ("mono" means one or single, thus one pole). • Magnets always have both north and south poles. The reason why monopole magnets don’t exist is because the north and south poles are created by the alignment of the molecules inside. They are all aligned in the direction of the north pole, so even if a magnet is broken in half, the alignment of the molecules has not changed, so the north and south poles still exist. • Note: Some theorists believe that magnetic monopoles may have been made in the early Universe. So far, none have been detected. S N

29. Action at a Distance Explained Although two magnets may not be touching, they still interact through their magnetic fields. This explains the ‘action at a distance’, say of a compass. Opposite poles attract! Like repels like!

30. Magnetic Field Lines 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. For instance, in a compact bar magnet or "dipole," field lines spread out from one pole and converge towards the other, and of course, the magnetic force is strongest near the poles where they come together.

31. SOURCES OF MAGNETIC FIELDS There are many sources of magnetic fields, not just from a bar magnet, and many of them will be described in this presentation.

32. Field Lines … Around a Bar Magnet Around a Doughnut Magnet Around a Magnetic Sphere of Repelling Bars of Attracting Bars

33. BAR MAGNETS Bar magnets are metal bars that have magnetic properties. The magnetic field produced by a bar magnet flows from the north end to the south end. It is a permanent magnet. The Earth can be considered a bar magnet as well. It has a pair of geographical poles and magnetical poles. See next slide Bar magnet demo

34. EFFECTS OF MAGNETISM (CONT’D) As said in the previous slide, there is a net force if the particle moves in a direction not parallel to the magnetic field. The force on the particle is perpendicular to both v and B. But how do you figure out in which direction? See next slide ?

35. EFFECTS OF MAGNETISM (CONT’D) It is by something know as the “Right hand rule.” First hold out your right hand. Point your fingers in the direction of the velocity times the sign of the charge. Curl them towards the direction of the magnetic field. Stick out your thumb, and that will be the direction of the force on the particle.   Yellow line = F = Line pointing towards you  = Line pointing away from you Remember (AGAIN):F = qv * B Red = + charge Blue = - charge Purple = v Black line = B

36. EFFECTS OF MAGNETISM (CONT’D) In the last slide we mentioned the of the right hand rule. This is also true for an wire or other object with an electrical current flow through it, since a current is nothing more than a flow of positive (negative) charges. To use the right hand rule, simply replace v with the direction of the flow of the current. An equivalent equation for this is F = iL*B, where L is the length of the wire in meters that lies in the magnetic field. Try solving the problem on the right (the magnetic field is uniform). N i  S

37. EFFECTS OF MAGNETISM (CONT’D) ANSWER: N Now, let’s try this. Let’s say its length is 25 cm, and the current going through it is 5 A, but we don’t know the magnitude of the magnetic field, but we measure the force on the bar to be 10 N. What is the field strength?           i  ANSWER #2: 10 N = (5A)(0.25m)*B (10 N)/[(5A)(0.25m)] = B B = 8 N/A*m = 8 T S

38. IS LEVITATION POSSIBLE? Yes! Through the power of diametic plate strategically placed around an object. The reason any living creature has the ability to be levitated is because everything has the potential to be magnetic. We all have domains in our body, but ours are almost always randomly oriented. Magnetic levitation is also sometimes used by high speed “bullet” trains. Click on the links below to see a frog being levitated: http://theory.uwinnipeg.ca/mod_tech/node83.html

39. Scientists Can Be Famous, Too! Tesla

40. Famous, continued Gauss Faraday

41. APPLICATIONS IN SCIENCE Besides being used in motors and generators, there are many applications for magnets in scientific or medical devices. For example, magnets are used in MRI (magnetic resonance) scans, which are used to help diagnose medical conditions. Additionally, high-powered electromagnets are used in particle accelerators. Particle accelerators are huge machines used to accelerate subatomic particles to nearly the speed of light. Scientists study the interactions of different particles being smashed into each other at these high speeds.

42. Cyclotron • Developed in 1931 by E. O. Lawrence and M. S. Livingston at UC Berkeley • Uses electric fields to accelerate and magnetic fields to guide particles at very high speeds

43. How a Cyclotron Works • Pair of metal chambers shaped like a pillbox cut along one of its diameters (cleverly referred to as “D”s) and slightly separated • Ds connected to alternating current • Ions injected near gap • Ions are accelerated as long as they remain “in step” with alternating electric field

44. Simple Electric Generator (AC) Electric generators transform a torque into a current. As a rotating wire in a generator moves from a straight angle to a 90 degree angle relative to the magnetic field, the current increases to a maximum. When it then moves from a 90 degree angle to a straight angle, the induced electric current moves to zero. When the rotating wire continues to move after reaching a straight angle, it begins to create a current flowing in the opposite direction. When the wire is once again at a 90 degree angle, this current is at a maximum, and when the wire is back to it’s starting position, the current is zero. This cycle repeats every time the wire makes a complete revolution, in a periodic manner.

45. AC Electric Generators (cont’d.) The simplest form of an electric generator is called an alternating current (or AC) generator. The current produced by an AC generator switches directions every time the wire inside of it is rotated to make a half turn. In standard generators in the United States, the generator has a frequency of 60Hz, which means the current switches direction 120 times every second! A graph of the current output from an AC generator produces a sinusoidal curve due to the periodic nature of the generator’s rotation. Animation of an AC generator.

46. Electric Motors • The same principles that allow an electric generator to function also work to allow an electric motor to function. • Electric motors are quite similar to electric generators, but work in the reverse fashion, generating a torque from an electric current. • In a simple AC electric motor, a current is fed into a wire rotor placed within the field of a magnet. • Remember that you can use the Right Hand Rule to determine the direction of the force due to the magnetic field on a current flowing through a wire. • Animation of a DC motor. In a DC motor running from an AC current, there is a mechanism called the commutator that switches the contacts from which the rotor is getting current from when the current switches directions, producing direct current in the rotor. Second animation.

47. AC Electric Motors (cont’d) When a current is fed into the wire rotor of a motor in a magnetic field, a force is felt on the two wires that do not line up with the magnetic field. They provide a torque on the wire loop and turn the loop. As the loop reaches a half turn, the current changes direction, and the torque continues in the same direction. This happens many times per second, causing the rotor to constantly turn. The turning of the rotor provides torque which can be harnessed to do work.

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

49. Magnetic Force on Current-Carrying Wire • Since moving charges experience a force in a magnetic field, a current-carrying wire will experience such a force, since a current consists of moving charges. This property is at the heart of a number of devices. • The magnetic field lines around an electrically charged wire form concentric rings. • The magnetic field of an infinitely long straight wire can be obtained by applying Ampere's law. The expression for the magnetic field is: µ0 I Where I is the current in the wire, r is the radial distance from the middle of the wire to the point where you are measuring the field and the permeability of free space is µ0= 4π × 10-7T·m∕A. B= 2πr

50. Electromagnets (Magnetism from Electricity) • Anything with an electrical current running through it has a magnetic field. • An electromagnet is simply a coil of wires which, when a current is passed through, generate a magnetic field, as below. • Solenoids are one the most common forms of electromagnets. • Solenoids consist of a tightly wrapped coil of wire around a core (usually iron). When a charge is applied to the coil, a magnetic field is produced. • As the coil becomes more tightly wrapped, the magnetic field becomes more concentrated inside the coil and less concentrated outside of it.