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Magnetism, electromagnetic induction, alternate current Talián Csaba Gábor PTE Med. School Inst. of Biophysics 06.11.2014. Empirical knowledge • Some iron ores attract other metal pieces • China – – e g. magnetite (Fe2+Fe23+O4) – – Earth-divining (→ Feng-shui) How many needles can it lift → quality categories Moving magnets always take one direction: navigation, difference of magnetic and astronomic Earth poles VII-X. century: compass Magnesia, Greek city in Asia Minor • England, ~ 1600 Earth is a big magnet William Gilbert (1544-1603, ENG) • Natural magnetic property can be transmitted to another steel object by touch (artificial magnet) • Magnet rod attracts other objects with its ends the most, barely with its middle part magnetic poles (pointlike impact centers), magnetic axis (Poles from the end of the rod ~ 1/12 distance) • Magnet freely rotating around an axis takes always the same direction → the poles are unlike („positive” and „negative”) • Unlike poles attract, like poles repel one another repulsion attraction • Two magnets positioned with their unlike poles cancel each other repulsion Magnetic influence • Softh iron temporary magnet • Steel permanent magnet • Magnet is like electric dipoles magnetic momentum: m = p*l (p: pole strength; an analogon to electric charge, a quantity proportional to the force/effect exerted by the magnet) • • By division new dipoles can be made The strength of the new pole equals the original one Elementary, separable magnetic monopoles, „charges” do not exist (theoretically predicted, but not found) • A metal rod contains many unoriented elementary magnets that cancel the effect of the others they can become oriented by an outer magnetic impact like a chain of electric dipoles orientation can remain or leave off + - + - + - Magnetic force • Model of the „magnetic charge”: one end of a very long and thin magnet rod ~ Coulomb’s law: = ∙ ∙ = ∙ ∙ ∙ p1, p2: magnetic pole strength, measure: V*s r: distance(vector) 10 ∙ 1 = = (4 ∙ ) ∙ 4 ∙ ∙ = 1,257 ∙ 10 ∙ ∙ (induction constant, permeability) Magnetic field • Every moving charged particle creates a magnetic field In an unorganized physical body they cancel each other • Magnetic field (force) exerts torque on other magnets in it: If a magnetic dipole stands in the direction of the outer magnetic then Mf = 0, so it gives the direction of the field at that place • Magnetic field lines run from the northern to the southern pole Magnetic field strength points in a tangential direction of the field lines • Magnetic field strength I. !" = # H= !$ % (A/m) Magnetic field strength II. (magnetic inducion vector ) (induction density): B Measure: Tesla (Vs/m2 = N/Am = 104 Gauss) Nicola Tesla (1856-1943, SRB-USA) Magnetic field of the electric current • Strong direct current through a conductor makes the compass needle turn (Ørsted, 1820) – – – – Electric current creates a magnetic field (Ampere’s law) Every moving charge in general Every substance has its magnetic field Reverting the direction of the current the shift of the pointer is opposite Hans Christian Ørsted (1777-1851, DEN) Nearly homogenous magnetic fields & = ' 2π )' & * ' & 2 & )' 2 North északi pole pólus I Righ hand rule Effect of the magnetic field on conductors • • On conductors carrying current a force is acting in a magnetic field Proportional to the angle between the direction of the current and the magnetic field strength (ϕ) '*&+,- ./ '01&+,- 1. EXERCISE: MAGNETIC FIELD OF THE ELECTRIC CURRENT In a coil the number of turns is 13, the distance betwen them is 0,4 cm. A wire frame of 8 cm edge length is located in the coil, parallel to the longitudinal axis. If 1,5 A current is coupled on both the coil and the frame, what is the torque acting on the frame? )' & * & 1,257 ∙ 10 ∙ 13 ∙ 1,5 ∙ 5,1 ∙ 104 5 ∙ 0,048 ./ '01&+,- ./ 1,5 ∙ 0,08 ∙ 5,1 ∙ 104 5 4,9 ∙ 10 ) ∙ & = ' 2 ' *& Modern definition of current(1948) ' ' * 2 Effect of the magnetic field on moving charges • Lorentz’s force: = 7[9:] An opposite direction on negative charges! Hendrik Lorentz (1853-1928, NED) B and v perpendicular not perpendicular Devices working by the magnetic effect of current • Galvanometer DC Ammeter with a turning coil also AC Electrodynameter also AC • Electromagnet • Electric bell Loudspeaker Relay and interrupter Cathode ray tube, television Mass spectrometer Electronmicroscope 2. EXERCISE: LORENTZ’S FORCE What is the radius of orbit of an electron accelerated to 1 eV kinetic energy in a magnetic field perpendicular to its direction of movement, if the magnetic field strength is 0,5 T? The mass of the electron is 9,11·10-31 kg. ∙ < 7∙<∙& ∙< 7∙& < 5,93 ∙ 10= 9,11·10−31 kg ∙ 5,93 ∙ 10= 6,75 ∙ 10 ? 1,6 ∙ 10 ∙ 0,55 Electromagnetic induction • Motional induction: relative displacement of a conductor in a magnetic field induces electric current in the conductor • Conductional induction: magnetic field strength is chanching around a conductor • • Magnetic flux passing the area around the conductor is changing in time Voltage (current) is proportional to the rate of the change: @ &*< @ AΦ⁄AC A&⁄AC • Lenz’s law : direction of the induced current is so that it impedes the effect that causes it Heinrich Lenz (1804-1865, GER) Alternate current • Loop or coil rotated in a homogenous magnetic field @ @EFG sin HC @I// @EFG / 2 • Modern generator rotating magnet, voltage is generated on the stator • Electric motor: works in an inverted principle: Current is coupled on the conductor in a magnetic field so it comes into motion Serial RLC circuit • • • Ohmic resistance: the same against alternate current as direct current Self-inducing coil: higher resistivity against alternate current proportionally to inductivity ‚L’ and frequence ‚f’ Capacitor: lower resistivity against alternate current proportionally to capacitance ‚C’ and frequence ‚f’ @ J' + L M A' 7 + AC J + (LH − Impedance 1 ) H HOMEWORK What is the effective voltage of the electric motor whose square-shaped rotor has 30 cm as length and it makes 12.000 revolutions per minute in a magnetic field of 0,25 T strength? H =2∙∙S = * 0,3 → = 0,15 <PFQR = ∙ H = 0,15 ∙ 1256 @EFG 1 2 ∙ ∙ 12000 +, 1 = 188,4 = & ∙ * ∙ < = 0,255 ∙ 0,3 ∙ 188,4 = 14,13 @I// = @EFG 2 = 14,13 = 10 1,414 60 1 = 1256