Magnetic Fields and Forces February 13 th , 2013

1. Chapter 20 Magnetic Fields and Forces February 13th, 2013

2. REVISED!!!!!room assignments for exam 1, 2, 3: Sections 302, 307, 309, 314, 323, 324 (TAs Lau & Woods) meet in 145 Birge Sections 305, 310, 312, 317, 321 (TAs Dodd & Lee) meet in 2103 Chamberlin Sections 301, 303, 311, 315, 319, 327, 328 (TAs Aggarwal, Osborne & Pankhuri) meet in 204 Education Sciences Sections 304, 306, 313, 316, 320, 322, 326 (TAs Kim, Patel & Ramesh) meet in B102 Van Vleck

3. review sessions to prepare for exam 1 All review sessions are 2 hours Saturday, Feb 16th, 10:00 AM, Chamberlin 3320, Pankhuri Saturday, Feb 16th, 5:00 PM, Chamberlin 3320, Hiren Patel Monday, Feb 18th, 10:00 AM, Chamberlin 3328, James Osborne Monday, Feb 18th, 4:35 PM, Chamberlin 3320, Jungha Kim Monday, Feb 18th, 4:35 PM, Chamberlin 3328, Nate Woods Tuesday, Feb 19th, 7:45 AM, Chamberlin 3320, Laura Dodd Tuesday, Feb 19th, 12:05 PM, Chamberlin 3328, Subin Lee Tuesday, Feb 19th, 2:25 PM, Chamberlin 3328, NitinRamesh Wednesday, Feb 20th, 12:00 PM, Chamberlin 3320, Greg Lau Wednesday, Feb 20th, 4:350 PM, Chamberlin 3328, Abhishek Aggarwal

4. Right Hand Rules, Summary • Right-hand rule number 1: to find the direction of the magnetic field from an electric current • Place the thumb of your right hand along the direction of the current • Curl your fingers to encircle the wire • The direction of the magnetic field lines is knuckle-to-finger tips • Right-hand rule number 2: to find the direction of the magnetic force (Lorentz force) on a moving charge or a current-carrying wire • Point the fingers of your right hand along the direction of the velocity • Curl your fingers towards the direction of the field • Curl your fingers through the smallest angle that connects the velocity and the field • If q is positive, the magnetic force is parallel to your thumb. If q is negative, the magnetic force is in the opposite direction

5. Magnetic Force on a wire • An electric current is a collection of moving charges, thus a magnetic force acts on a current • From the equation of the force on a moving charge, the force on a current-carrying wire is Fonwire = I L B sin θ • The direction of the force is given by the right-hand rule 2

6. demo: current in a wire, in the jaws of 2 horseshoe magnets I = 45 A VDC = 30 V Fon wire = I L B sin θ

7. Problem 20.47 A long, straight wire of length 0.75 m carries a current I = 1.5 A in a region where B = 2.3 T. If the force on the wire is 1.4 N, what is the angle between the field and the wire?

8. Torque on a Current Loop • B produces a torque on a current loop • Use right-hand rule 2 to find F directions • On sides 2 and 4 F = 0 • On sides 1 and 3 are F1 and F3 are in opposite directions and produce a torque on the loop

9. Torque, cont. If the angle between the loop normal and the field is θ, and the loop is square, the torque is τ = I L2B sin θ For different shapes (rectangle, circle) of area A, this becomes τ = IA B sin θ

10. demo: Galvanometers measure current using the torque on a loop I = 12A VDC = 3 V Inverting the current makes the loop rotate in the opposite direction τ= IA B sin θ

11. Ampère’s Law • Relates the magnetic field along a path to the electric current enclosed by the path

12. Ampère’s Law, cont. = • For the path shown in fig. 20.30, Ampère’s Law states that • μo is the permeability of free space • μo = 4 π× 10-7 T .m / A • If B varies along the path, Ampère’s Law cannot be used

13. B near a Long Straight Wire Ampère’s Law B|| is the same all along the path If the circular path has a radius r, then the total path length is 2 πr

14. B inside Current Loop • It is not possible to find a path along which the magnetic field is constant • So Ampère’s Law cannot be easily applied • From other techniques, the field at the center of the loop is

15. A Solenoid is a series of loops This is valid for a solenoid with a length much greater than the diameter

16. Question 20.11 To make sure most people fit, we make L= 2.5 m, and R = 0.75 m We know that the magnetic field is B = 1 T We know that the current is I = 100 A Magnetic Resonance Imaging (MRI) uses the magnetic field produced by a large solenoid to obtain images from inside living tissue. The solenoid is large enough to accommodate a person inside. Assuming the inside field is 1 T, design an MRI solenoid. Estimate the necessary length and radius, assuming that the wire can carry currents as high as 100 A. How many turns must the solenoid have to produce the desired field? We use the equation for the magnetic field inside a solenoid (Equation 20.24) and solve for the number of turns, N. We then plug in the numbers 16

17. Hall Effect The same I can be produced by • + charges moving to the right • - charges to the left • The Hall Effect can distinguish between the two options

18. Hall Effect • Place a current-carrying wire in a magnetic field directed perpendicular to the current • With + carriers, + charges accumulate on the top side of the wire • With - carriers, - charges accumulate on the top side of the wire • V across wire distinguishes + or - charge carriers producing the current

19. Blood-Flow Meter • Measures the blood velocity in arteries during surgery • Blood contains ions • A magnetic field is applied to the artery • The resulting potential difference across the artery can be measured • Blood velocity can be measured

20. Relays • The field produced by a solenoid can be made larger by filling it with a magnetic material • A magnetic force is exerted on the moveable part of the switch • A small current through the solenoid can control a much larger current through the switch

21. Speakers • A speaker uses a solenoid coil wrapped around a magnetic material • The current varies according to the amplitude and frequency of the music • The solenoid vibrates, causing the speaker cone to produce sound

22. Electric Motor • A magnetic field can produce a torque on a current loop • If the loop is attached to a rotating shaft, an electric motor is formed • In a practical motor, a solenoid is used instead of a single loop • Additional set-up is needed to keep the shaft rotating

23. Electric Generator • Electric generators are closely related to motors • A generator produces an electric current by rotating a coil between the poles of the magnet • A motor in reverse

24. Magnetic Bacteria • Magnetotactic bacteria possess small grains of iron called magnetosomes • Each grain acts as a bar magnet • Bacteria use the magnetosomes to orient themselves with the Earth’s magnetic field • Allows them to determine up and down

25. Magnetic Dating • Reversals in the Earth’s magnetic field can be used to date past events • Dates of more than 25 reversals are known

26. Velocity-Dependent Force • The magnetic force exerted on a moving charged particle is dependent on its velocity • Differs from gravitational and electrical forces • The two observers shown both agree the particle is accelerated, but only observer 1 says there is a magnetic force acting on the particle

27. Velocity-Dependent Force, cont. Special relativity solves the dilemma Observer 2 will actually say the particle experiences an electric force This shows a deep connection between electric and magnetic forces The connect is a critical part of the theory of electromagnetism

28. Magnetic Moment • For a current loop, the magnetic moment is IA • The direction of the magnetic moment is either along the axis of the bar magnet or perpendicular to the current loop • The strength of the torque depends on the magnitude of the magnetic moment

29. Mass Spectrometer • Allows for the separation of ions according to their mass or charge • The ions enter with some speed v • They pass into a region where the magnetic field is perpendicular to the velocity

30. Mass Spectrometer, cont. • The ions travel in a circle in the mass spectrometer • The radius of the circle is mv/qB • Ions with different masses will travel in arcs with different radii • Mass spectrometer can also be used to find the composition of a material • Measure the values of v, B and r • Calculate q/m • Charge to mass ratio