Electricity and Magnetism Magnetism Application of magnetic forces Ampere’s law

1. Electricity and Magnetism • Magnetism • Application of magnetic forces • Ampere’s law /

2. 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?

3. Magnetic Field of the Earth

4. 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. 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?

6. 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

7. I F B B F a/2 b F F a 19.5 Torque on a Current Loop • Imagine a current loop in a magnetic field as follows:

8. I F B B F a/2 b F F a

9. In a motor, one has “N” loops of current

10. Example 1 : Torque on a circular loop in a magnetic field 30.0o 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

11. 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.

12. 19.6 Galvanometer/Applications Device used in the construction of ammeters and voltmeters. Scale Current loop or coil Magnet Spring

13. 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. 60 W Galvanometer Rp

14. 60 W Galvanometer 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!

15. 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 60 W Galvanometer

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

17. q v F 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. ´ ´´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ ´ r

18. The magnetic force produces a centripetal acceleration. The particle travels on a circular trajectory with a radius:

19. 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

20. 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.

21. I=0 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

22. 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

23. Magnitude of the field I r B mo called the permeability of free space

24. 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 B Dl

25. Consider a case where B is constant and uniform. Then one finds: