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General Physics (PHY 2140) Lecture 13 Electricity and Magnetism Magnetism Application of magnetic forces Ampere’s law http://www.physics.wayne.edu/~apetrov/PHY2140/ Chapter 19 5/23/2017 1 Lightning Review Last lecture: 1. Magnetism Magnetic field Magnetic force on a moving particle Magnetic force on a current F qvB sin F BIl sin Review Problem: How does the aurora borealis (the Northern Lights) work? 5/23/2017 2 Magnetic Field of the Earth 5/23/2017 3 Review Problem 2 How 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. 5/23/2017 4 Review Example 1: Flying duck A 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? 5/23/2017 5 Review Example 2: Wire in Earth’s B Field 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, and has a magnitude of 0.50 x 10-4 T. Find the magnetic force on a 36-m length of wire. What happens if the direction of the current is reversed? B=0.50 x 10-4 T. I = 22 A l = 36 m Fmax = BIl 5/23/2017 Fmax BIl 0.50 104 T 22 A 36m 4.0 102 N 6 19.5 Torque on a Current Loop Imagine a current loop in a magnetic field as follows: I B B F F a/2 b F F a 5/23/2017 7 I B B F F a/2 b F F a F1 F2 BIb max F1 a2 F2 a2 BIb a2 BIb a2 max BIba BIA BIAsin 5/23/2017 8 In a motor, one has “N” loops of current NBIAsin 5/23/2017 9 Example 1 : Torque on a circular loop in a magnetic field A circular loop of radius 50.0 cm is oriented at an angle of 30.0o to a magnetic field of 0.50 T. The current in the loop is 2.0 A. Find the magnitude of the torque. r = 0.500 m = 30o B = 0.50 T I = 2.0 A N=1 5/23/2017 30.0o B NBIA sin 2 0.50T 2.0 A 0.50m sin 30.0o 0.39 Nm 10 Example 2: triangular loop A 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. 5/23/2017 11 19.6 Galvanometer/Applications Device used in the construction of ammeters and voltmeters. Scale Current loop or coil Magnet 5/23/2017 Spring 12 Galvanometer used as Ammeter Typical galvanometer have an internal resistance of the order of 60 W - that could significantly disturb (reduce) a current measurement. Built to have full scale for small current ~ 1 mA or less. Must therefore be mounted in parallel with a small resistor or shunt resistor. Galvanometer 60 W Rp 5/23/2017 13 Galvanometer 60 W 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. 0.001A 60W 1.999 A Rp R p 0.03002W • Rp is rather small! • The equivalent resistance of the circuit is also small! 5/23/2017 14 Galvanometer 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. Rs 5/23/2017 Galvanometer 60 W 15 Rs Galvanometer 60 W Maximum voltage across galvanometer: Vmax 0.001A 60W 0.06V Suppose one wish to have a voltmeter that can measure voltage difference up to 100 V: 100V 0.001A Rp 60W Rp 99940W 5/23/2017 Large resistance 16 19.7 Motion of Charged Particle in magnetic field Consider positively charge particle moving in a uniform magnetic field. q Suppose the initial velocity of the particle is perpendicular to v the direction of the field. Then a magnetic force will be exerted on the particle and make follow a circular path. 5/23/2017 F r Bin 17 The magnetic force produces a centripetal acceleration. mv 2 F qvB r The particle travels on a circular trajectory with a radius: mv r qB 5/23/2017 18 Example 1 : Proton moving in uniform magnetic field A proton is moving in a circular orbit of radius 14 cm in a uniform magnetic field of magnitude 0.35 T, directed perpendicular to the velocity of the proton. Find the orbital speed of the proton. r = 0.14 m B = 0.35 T m = 1.67x10-27 kg q = 1.6 x 10-19 C mv r qB 5/23/2017 qBr v m 1.6 1019 C 0.35T 14 102 m 1.67 1027 kg 4.7 106 m s 19 Example 2: Consider the mass spectrometer. The electric field between the plates of the velocity selector is 950 V/m, and the magnetic fields in both the velocity selector and the deflection chamber have magnitudes of 0.930 T. Calculate the radius of the path in the system for a singly charged ion with mass m=2.18×1026 kg. 5/23/2017 20 19.8 Magnetic Field of a long straight wire Danish scientist Hans Oersted (1777-1851) discovered somewhat by accident that an electric current in a wire deflects a nearby compass needle. In 1820, he performed a simple experiment with many compasses that clearly showed the presence of a magnetic field around a wire carrying a current. I=0 5/23/2017 I 21 Magnetic Field due to Currents The passage of a steady current in a wire produces a magnetic field around the wire. Field form concentric lines around the wire Direction of the field given by the right hand rule. If the wire is grasped in the right hand with the thumb in the direction of the current, the fingers will curl in the direction of the field. Magnitude of the field I o I B 2 r 5/23/2017 22 Magnitude of the field o I B 2 r I r B o called the permeability of free space o 4 10 Tm / A 7 5/23/2017 23 Ampere’s Law Consider a circular path surrounding a current, divided in segments l, Ampere showed that the sum of the products of the field by the length of the segment is equal to o times the current. B l I Andre-Marie Ampere I o r l 5/23/2017 B 24 Consider a case where B is constant and uniform. B l B l B 2 r I o Then one finds: o I B 2 r 5/23/2017 25