Chapter 27Magnetic FieldsA Brief History of Magnetism13thcentury BCChinese used a compassUses a magnetic needleProbably an invention of Arabic or Indian origin800 BCGreeksDiscovered magnetite (Fe3O4) attracts pieces of ironA Brief History of Magnetism, 21269Pierre de Maricourt found that the direction of a needle near a spherical natural magnet formed lines that encircled the sphere The lines also passed through two points diametrically opposed to each otherHe called the points polesA Brief History of Magnetism, 31600William GilbertExpanded experiments with magnetism to a variety of materialsSuggested the Earth itself was a large permanent magnetA Brief History of Magnetism, 41819Hans Christian OerstedDiscovered the relationship between electricity and magnetismAn electric current in a wire deflected a nearby compass needleA Brief History of Magnetism, final1820’sFaraday and HenryFurther connections between electricity and magnetismA changing magnetic field creates an electric fieldMaxwellA changing electric field produces a magnetic fieldMagnetic PolesEvery magnet, regardless of its shape, has two polesCalled north and south polesPoles exert forces on one anotherSimilar to the way electric charges exert forces on each otherLike poles repel each otherN-N or S-SUnlike poles attract each otherN-SMagnetic Poles, cont.The poles received their names due to the way a magnet behaves in the Earth’s magnetic fieldIf a bar magnet is suspended so that it can move freely, it will rotateThe magnetic north pole points toward the Earth’s north geographic poleThis means the Earth’s north geographic pole is a magnetic south poleSimilarly, the Earth’s south geographic pole is a magnetic north poleMagnetic Poles, finalThe force between two poles varies as the inverse square of the distance between themA single magnetic pole has never been isolatedIn other words, magnetic poles are always found in pairsAll attempts so far to detect an isolated magnetic pole has been unsuccessfulNo matter how many times a permanent magnetic is cut in two, each piece always has a north and south poleMagnetic FieldsReminder: an electric field surrounds any electric chargeThe region of space surrounding any movingelectric charge also contains a magnetic fieldA magnetic field also surrounds a magnetic substance making up a permanent magnetMagnetic Fields, cont.A vector quantitySymbolized byDirection is given by the direction a north pole of a compass needle points in that locationMagnetic field lines can be used to show how the field lines, as traced out by a compass, would lookBrMagnetic Field Lines, Bar Magnet ExampleThe compass can be used to trace the field linesThe lines outside the magnet point from the North pole to the South poleUse the active figure to trace the field linesPLAYACTIVE FIGUREMagnetic Field Lines, Bar MagnetIron filings are used to show the pattern of the electric field linesThe direction of the field is the direction a north pole would pointMagnetic Field Lines, Unlike PolesIron filings are used to show the pattern of the electric field linesThe direction of the field is the direction a north pole would pointCompare to the electric field produced by an electric dipoleMagnetic Field Lines, Like PolesIron filings are used to show the pattern of the electric field linesThe direction of the field is the direction a north pole would pointCompare to the electric field produced by like chargesDefinition of Magnetic FieldThe magnetic field at some point in space can be defined in terms of the magnetic force, The magnetic force will be exerted on a charged particle moving with a velocity, Assume (for now) there are no gravitational or electric fields presentBFrvrForce on a Charge Moving in a Magnetic FieldThe magnitude FBof the magnetic force exerted on the particle is proportional to the charge, q, and to the speed, v, of the particleWhen a charged particle moves parallel to the magnetic field vector, the magnetic force acting on the particle is zeroWhen the particle’s velocity vector makes any angle θ≠ 0 with the field, the force acts in a direction perpendicular to both the velocity and the fieldFBon a Charge Moving in a Magnetic Field, finalThe magnetic force exerted on a positive charge is in the direction opposite the direction of the magnetic force exerted on a negative charge moving in the same directionThe magnitude of the magnetic force is proportional to sin θ, where θis the angle the particle’s velocity makes with the direction of the magnetic fieldMore About Directionis perpendicular to the plane formed by andOppositely directed forces exerted on oppositely charged particles will cause the particles to move in opposite directionsBFrvrBrForce on a Charge Moving in a Magnetic Field, FormulaThe properties can be summarized in a vector equation:is the magnetic forceq is the chargeis the velocity of the moving chargeis the magnetic fieldBq= ×F v Br rrBFrvBrDirection: Right-Hand Rule #1The fingers point in the direction of comes out of your palmCurl your fingers in the direction of The thumb points in the direction of which is the direction of vrBrBr×v BrrBFrDirection: Right-Hand Rule #2Alternative to Rule #1Thumb is in the direction of Fingers are in the direction of Palm is in the direction ofOn a positive particleYou can think of this as your hand pushing the particlevrBrBFrMore About Magnitude of FThe magnitude of the magnetic force on a charged particle is FB= |q| v B sin θθ is the smaller angle between v and BFBis zero when the field and velocity are parallel or antiparallelθ = 0 or 180oFBis a maximum when the field and velocity are perpendicularθ = 90oDifferences Between Electric and Magnetic FieldsDirection of forceThe electric force acts along the direction of the electric fieldThe magnetic force acts perpendicular to the magnetic fieldMotionThe electric force acts on a charged particle regardless of whether the particle is movingThe magnetic force acts on a charged particle only when the particle is in motionMore Differences Between Electric and Magnetic FieldsWorkThe electric force does work in displacing a charged particleThe magnetic force associated with a