General Physics (PHY 2140) Lecture 13 Electricity and Magnetism Application of magnetic forces Ampere’s law http://www.physics.wayne.edu/~apetrov/PHY2140/ Chapter 19 9/16/2018

Lightning Review Last lecture: Magnetism Magnetic field Magnetic force on a moving particle Magnetic force on a current Review Problem: How does the aurora borealis (the Northern Lights) work? 9/16/2018

Magnetic Field of the Earth 9/16/2018

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. 9/16/2018

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? 9/16/2018

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 9/16/2018

19.5 Torque on a Current Loop Imagine a current loop in a magnetic field as follows: B I b a a/2 F 9/16/2018

I F B B F a/2 b F F a 9/16/2018

In a motor, one has “N” loops of current 9/16/2018

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. B r = 0.500 m q = 30o B = 0.50 T I = 2.0 A N = 1 9/16/2018

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. 9/16/2018

19.6 Galvanometer/Applications Device used in the construction of ammeters and voltmeters. Scale Current loop or coil Magnet Spring 9/16/2018

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 9/16/2018

The equivalent resistance of the circuit is also small! 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. Rp is rather small! The equivalent resistance of the circuit is also small! 9/16/2018

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 Galvanometer 60 W 9/16/2018

Maximum voltage across galvanometer: 60 W Rs Maximum voltage across galvanometer: Suppose one wish to have a voltmeter that can measure voltage difference up to 100 V: Large resistance 9/16/2018

19.7 Motion of Charged Particle in magnetic field Bin Consider positively charge particle moving in a uniform magnetic field. Suppose the initial velocity of the particle is perpendicular to the direction of the field. Then a magnetic force will be exerted on the particle and make follow a circular path. ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ F v q r 9/16/2018

The magnetic force produces a centripetal acceleration. The particle travels on a circular trajectory with a radius: 9/16/2018

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 9/16/2018

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=2.18×10-26 kg. 9/16/2018

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 I 9/16/2018

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 9/16/2018

mo called the permeability of free space Magnitude of the field I r B mo called the permeability of free space 9/16/2018

Ampere’s Law Consider a circular path surrounding a current, divided in segments Dl, Ampere showed that the sum of the products of the field by the length of the segment is equal to mo times the current. Andre-Marie Ampere I r Dl B 9/16/2018

Consider a case where B is constant and uniform. Then one finds: 9/16/2018