Slide 1Lightning ReviewMagnetic Field of the EarthReview Problem 2Review Example 1: Flying duckReview Example 2: Wire in Earth’s B Field19.5 Torque on a Current LoopSlide 8Slide 9Example 1 : Torque on a circular loop in a magnetic fieldExample 2: triangular loop19.6 Galvanometer/ApplicationsGalvanometer used as AmmeterSlide 14Slide 15Slide 1619.7 Motion of Charged Particle in magnetic fieldSlide 18Example 1 : Proton moving in uniform magnetic fieldExample 2:19.8 Magnetic Field of a long straight wireMagnetic Field due to CurrentsSlide 23Slide 24Slide 251101/14/1901/14/19General Physics (PHY 2140)Lecture 13Lecture 13 Electricity and MagnetismMagnetismApplication of magnetic forces Ampere’s lawChapter 19http://www.physics.wayne.edu/~apetrov/PHY2140/2201/14/1901/14/19Lightning ReviewLightning ReviewLast lecture: 1.1.MagnetismMagnetismMagnetic fieldMagnetic fieldMagnetic force on a moving particleMagnetic force on a moving particleMagnetic force on a currentMagnetic force on a currentReview Problem: How does the aurora borealis (the Northern Lights) work? sinF qvB q=sinF BIl q=3301/14/1901/14/19Magnetic Field of the EarthMagnetic Field of the Earth4401/14/1901/14/19Review Problem 2Review Problem 2How does your credit card work?The stripe on the back of a credit card is a magnetic stripe, often called a magstripe. The magstripe is made up of tiny iron-based magnetic particles in a plastic-like film. Each particle is really a tiny bar magnet about 20-millionths of an inch long. The magstripe can be "written" because the tiny bar magnets can be magnetized in either a north or south pole direction. The magstripe on the back of the card is very similar to a piece of cassette tape .A magstripe reader (you may have seen one hooked to someone's PC at a bazaar or fair) can understand the information on the three-track stripe.5501/14/1901/14/19Review Example 1: Flying duckReview Example 1: Flying duckA duck flying horizontally due north at 15 m/s passes over Atlanta, where the magnetic field of the Earth is 5.0×10-5T in a direction 60° below a horizontal line running north and south. The duck has a positive charge of 4.0×10-8C. What is the magnetic force acting on the duck?6601/14/1901/14/19Review Example 2: Wire in Earth’s B FieldReview Example 2: Wire in Earth’s B FieldA wire carries a current of 22 A from east to west. Assume that at this location A wire carries a current of 22 A from east to west. Assume that at this location the magnetic field of the earth is horizontal and directed from south to north, the magnetic field of the earth is horizontal and directed from south to north, and has a magnitude of 0.50 x 10and has a magnitude of 0.50 x 10-4-4 T. Find the magnetic force on a 36-m length T. Find the magnetic force on a 36-m length of wire. What happens if the direction of the current is reversed?of wire. What happens if the direction of the current is reversed?B=0.50 x 10-4 T. I = 22 Al = 36 mFmax = BIl( )( ) ( )max420.50 10 22 364.0 10F BIlT A mN--= �== �7701/14/1901/14/1919.5 Torque on a Current Loop19.5 Torque on a Current LoopImagine a current loop in a magnetic field as follows:Imagine a current loop in a magnetic field as follows:BIbaBa/2FFFF8801/14/1901/14/19BIbaBa/2FFFF1 2F F BIb= =( ) ( )max 1 22 2 2 2a a a aF F BIb BIbt = + = +maxBIba BIAt = =sinBIAt q=9901/14/1901/14/19sinN B IAt q=In a motor, one has “N” loops of current101001/14/1901/14/19Example 1 : Torque on a circular loop in a Example 1 : Torque on a circular loop in a magnetic fieldmagnetic fieldA circular loop of radius 50.0 cm is oriented at an A circular loop of radius 50.0 cm is oriented at an angle of 30.0angle of 30.0oo to a magnetic field of 0.50 T. The to a magnetic field of 0.50 T. The current in the loop is 2.0 A. Find the magnitude of the current in the loop is 2.0 A. Find the magnitude of the torque.torque.B30.0or = 0.500 m = 30oB = 0.50 TI = 2.0 AN = 1( ) ( ) ( )2sin0.50 2.0 0.50.390 sin 30.0oNBIAT A mNmt qpt=� �=� �=111101/14/1901/14/19Example 2: triangular loopExample 2: triangular loopA 2.00m long wire carrying a current of 2.00A forms a 1 turn loop in the shape of an equilateral triangle. If the loop is placed in a constant magnetic field of magnitude 0.500T, determine the maximum torque that acts on it.121201/14/1901/14/1919.6 Galvanometer/Applications19.6 Galvanometer/ApplicationsDevice used in the construction Device used in the construction of ammeters and voltmeters.of ammeters and voltmeters.MagnetCurrent loop or coilSpringScale131301/14/1901/14/19Galvanometer used as AmmeterGalvanometer used as AmmeterTypical galvanometer have an internal resistance of the order of Typical galvanometer have an internal resistance of the order of 60 W - that could significantly disturb (reduce) a current 60 W - that could significantly disturb (reduce) a current measurement.measurement.Built to have full scale for small current ~ 1 mA or less. Built to have full scale for small current ~ 1 mA or less. Must therefore be mounted in parallel with a small resistor or Must therefore be mounted in parallel with a small resistor or shunt resistor.shunt resistor.Galvanometer60 Rp141401/14/1901/14/19Galvanometer60 Rp•Let’s convert a 60 W, 1 mA full scale galvanometer to an ammeter that can measure up to 2 A current.•Rp must be selected such that when 2 A passes through the ammeter, only 0.001 A goes through the galvanometer.( ) ( ) ( )0.001 60 1.9990.03002ppA A RRW == W•Rp is rather small!•The equivalent resistance of the circuit is also small!151501/14/1901/14/19Galvanometer used as Voltmeter•Finite internal resistance of a galvanometer must also addressed if one wishes to use it as voltmeter. •Must mounted a large resistor in series to limit the current going though the voltmeter to 1 mA.•Must also have a large resistance to avoid disturbing circuit when measured in parallel.Galvanometer60 Rs161601/14/1901/14/19Galvanometer60 RsMaximum voltage across galvanometer:( ) ( )max0.001 60 0.06V A VD = W =Suppose one wish to have a voltmeter that can measure voltage difference up to 100 V:( )( )100 0.001 6099940ppV A RR= + W= WLarge resistance171701/14/1901/14/1919.7 Motion of Charged Particle in magnetic field19.7 Motion of Charged Particle in magnetic fieldConsider positively charge Consider positively charge particle moving in a uniform particle moving in a uniform magnetic field.magnetic field.Suppose the initial velocity of Suppose