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20 Magnetic Field and Magnetic Forces.pdf

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Wagih Ghobriel

Lecture Notes 20 Magnetic Field and Magnetic Forces Goals ■ To observe and visualize magnetic fields and forces. ■ To study the motion of a charged particle in a magnetic field. ■ To evaluate the magnetic force on a current-carrying conductor. ■ To determine the force and torque produced with a magnet and current-carrying loop of wire (the DC motor). ■ To study the fields generated by long, straight conductors. ■ To observe the changes in the field with the conductor in loops (forming the solenoid). ■ To calculate the magnetic field at selected points in space. ■ To understand magnetism via magnetic moments. Historical Notes - Lodestone (magnetite mineral):  The name "magnet" comes from lodestones found in a place called Magnesia.  A piece of intensely magnetic magnetite that was used as an early form of magnetic compass.  Only magnetite with a particular crystalline structure, lodestone, can act as a natural magnet and attract and magnetize ironn China, the earliest literary reference to magnetism lies in a 4ry BC book called Book of the Devil Valley Master: "The lodestone makes iron come or it attracts it." The earliest mention of the attraction of a needle appears in a work composed between 20 and 100AD.  From amusement and magic-like to application − “leading stone” (lodestone) – compasths and navigation  By the 12 century the Chinese were known to use the lodestone compass for navigation.  Today’s powerful lodestones − and magnetic materials are ubiquitous. What if no lodestones existed? ► The Chinese would certainly not have invented the magnetic compass. ► Magnetism would have been discovered much later, and one wonders how. ► Lacking the compass, the great voyages of discovery could hardly have taken place--Columbus, De Gama, Magellan and the rest. ► The history of the world might have been quite different! Magnetic Jewellery • Magnetic energy is the strongest natural force in the universe and the power of magnets is one of the most basic powers of nature. • The use of magnet therapy for health and well-being has an ancient history dating back thousands of years. • Ancient Egyptians used loadstones to prolong life and improve health. It is said that Cleopatra wore a polished lodestone on her third eye, in the belief that it helped maintain her youth and beauty. • In more recent times, Paracelsus (1493-1541) considered to be the father of modern medicine, believed that the "life force' of the body was most influenced by the force found in magnets. • In Europe, Russia, China, Japan and many other countries, convinced of the benefits, millions of people continue to use magnet therapy. • Today, we are experiencing an exciting revival of this ancient therapy. Resulting from the impact of more and more clinical studies and anecdotal evidence, 120 million people worldwide spend over $1.5 billion globally on the therapeutic benefits of magnets. Two experiments, different scale: Although the magnet on the left is an electromagnet (huge) and the one on the right is a permanent magnet (small), the idea is the same. Observations: ► Youget a hint of magnetic field whenever you attach a note to a refrigerator door with a small magnet. ► Accidentally erase a computer disk by bringing it near a magnet. ► Creditcards, VCRs,…etc ► A familiar type of magnet: “electromagnets”. A wire coil is wound around an iron core and a current is sent through the coil. The strength of the magnetic field is determined by the size of the current.industry, such magnets are used for sorting scrap iron among many other things. ► Youare probably more familiar with “permanent magnets” (like the refrigerator- door type). They do not need current to have a magnetic field. ► Magnets: A magnet is an object made of certain materials which create a magnetic field. Electricity-Magnetism-Electromagnetism:  From these modest origins, the sciences of electricity and magnetism developed separately for centuriestil 1820AD.  In 1820, Oersted found a connection between them: an electric current in a wire can deflect a magnetic compass needle.  The new science of “electromagnetism”was developed by Faraday, Henry, and Maxwell (who, in the mid-19th century put electromagnetism on a sound theoretical basis)… 20.1 Magnetism The behavior of bar magnets ■ Notice the general behavior trends of attraction and repulsion, dipole or monopole.  The simplest magnetic structure that can exist is a magnetic dipole. Magnetic monopoles do not exist (as far as we know) ∴We cannot define the magnetic field as we do for the electric field (E=F /q.)  Magnetic properties of materials can be traced back to their atoms and electrons.  The clustering of the lines (of e.g. iron filings) at the ends of a magnet suggests that one end is a “source” of the lines (the field diverges from it) and the other end is a “sink” of the lines (the field converges toward it).  By convention: north pole and south pole, respectively. The magnet with its two poles is an example of a “magnetic dipole”. Note:A magnetized bar is magnetically weak in the middle Puzzle Determine which of the two bars is magnetized (without using any other material.) A compass will align with fields  The compass will align with whatever average field is strongest. As shown in figure, the field caused by the current in the wire is stronger than that any background field from the earth.  Absent the current-carrying wire, the compass would align with the earth’s magnetic field. This allows a consistent direction to be determined by someone with the need for navigation. Iron filings will align as a compass does  Each small filing lines up tangent to the field lines allowing a visual demonstration The magnetic field lines and pattern of iron filings in the vicinity of a bar magnet and the magnetic field lines in the gap of a horseshoe magnet. “Earth is a huge magnet” ● It can be represented by a huge bar magneo (a magnetic dipole.) (William Gilbert 1540-1603) ● The dipole axis makes an angle about 11.5 with the rotation axis. ● It intersects Earth’s surface at the “geomagnetic north poand the“geomagnetic south pole”. ● The “north magnetic pole” is really the south pole of Earth’s magnetic dipole. ■ Our Earth itself has a magnetic field This field is not very strong but it is consistent. o ● The “field declination” is the angle (left or right) between geographic north (which is toward 90 latitude) and the horizontal component of the field. The “field inclination” is the angle (up or down) between a horizontal plane and the field’s direction. ● We can use a “compass” and a “dip meter” to determine these two angles. ● The field observed at any location on the surface of Earth varies with time. In fact, Earth’s field has reversed its polarity about every million years. Examples of Magnetic Fields  Fields are created in a variety of ways and observed in a variety of places. 20.2 Magnetic Field and Magnetic Force Magnetic Forces External Forces  Gravitational Force  Normal Force  Frictional Forces Newton’s  Tension Force Second Law  Restoring Force of a Spring ΣF = m a  Collisional Forces  Electrostatic Force  Magnetic Force The magnetic force, like the other forces we have encountered, may contribute to the net force that acts on an object Review: When a charge is placed in an electric field, it experiences a force, according to   F = qE Definition of the magnetic field The “magnetic field B” at a point is along the tangent to a field line. Its direction is that of the force on the north pole of a bar magnet, or the direction in which a compass needle points. The strength of the field is proportional to the number of lines passing through a unit area normal to the field . Therefore , B is also called the “magnetic flux density” .  Thereare two ways to set up a magnetic field: (1)Moving electrically charged particles. (2)Elementary particles such as electrons have an intrinsic magnetic field around them; that is these fields are a basic characteristic of the particle, just as are their mass and electric charge (or lack of charge).  The magnetic fields of the electrons in certain materials add together to give a net magnetic field around the material. This is true for the material in permanent magnets (which is good, because they can then hold notes to a refrigerator door). In other materials, the magnetic fields of all the electrons cancel out, giving magnetic fieldsurrounding the material. This is true for the material in your body (which is also good, because otherwise you might be slammed up against a refrigerator door every time you passed by). The force that a magnetic field exerts on a moving charge  Experimentally, we find that when a charged particle (either alone or part of a current)moves through a magnetic field, a force due to the field can act on the particle. The following conditions must be met for a charge to experience a magnetic force when placed in a magnetic field: 1. The charge must be moving. 2. The velocity of the charge must have a component that is perpendicular to the direction of the magnetic field. The effect of an existing magnetic field on a charge depends on the charges direction of motion relative to the field. The magnetic force F on a particle with charge q and velocity v in a magnetic field B is perpendicular to both v and B and given by : F = q v × B (0 ≤≤φ 180 ) Its magnitude iF = q vB sinφ , where φ is the angle betweev and B . The SI unit of the magnetic field is thetesla ( T ) •Note that 1 T≡ N.s/(C.m), and since C/s = 1A, 1 T≡ 1 N/(A.m). •Since the tesla is a large unit, a (cgs) unit called the gauss ( G ) is often used where 1 T = 10 Some approximate magnetic fields At the surface of a neutron star 10 −8 At Earth’s surface 10−10, In interstellar space 10T Example 1 Magnetic Forces on Charged Particles Aproton in a particle accelerator has a speed of 5.0x10 6m/s. The proton encounters a magnetic field whose magnitude is 0.40 T and whose direction makes and angle of 30.0 degrees with respect to the proton’s velocity (see part (c) of the figure). Find (a) the magnitude and direction of the force on the proton and (b) the acceleration of the proton. (c) What would be the force and acceleration of the particle were an electron? (a) ( −19)( 6 ) ) ( ) F = qovBsinθ = 1.60×10 C 5.0 1× m s 0.40T sin30.0 = 1.× 10 N3 −13 (b) F 1.6×10 N 13 2 a= m = 1.67×10−27kg =9.6×10 m s p (c) Magnitude is the same, but direction is opposite. F 1.6×10 −1N 17 2 a = = −31 =1.8×10 m s me 9.11×10 kg The Right Hand Rule Right Hand Rule No. 1.  Extend the right hand so the fingers point along the direction of the magnetic field and the thumb points along the velocity of the charge. The palm of the hand then faces in the direction of the magnetic force that acts on a positive charge.  If the moving charge is negative, the direction of the force is opposite to that predicted by RHR-1. Using the right hand rule, one may determine the direction of the field produced by a moving positive charge. The effect of the sign of a moving charge The effect of the sign of a moving charge Positive and negative charges will feel opposite effects from a magnetic field. Motion of a charge in an electric field Motion of a charge in a magnetic field Concepts at a glance Electrostatic Magnetic Force Force Electric Magnetic Test Field Moving Field Charge Test Charge When a particle is subject to both electric and magnetic fields, the total force on it is: F = q ( E + v × B ) It is convenient to symbolize the direction of B as: × × × × × × × × ● ● ● ● ● ● ● ● ● × × × × × × × × ● ● ● ● ● ● ● ● ● × × × × × × × × ● ● ● ● ● ● ● ● ● × × × × × × × × ● ● ● ● ● ● ● ● ● B is into the page B is out of the page velocity selector Magnetic fields can alter ionic movement  A velocity selector is a device for measuring the velocity of a charged particle. It consists of a tube in which an electric field
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