1. Magnetic Force Physics 102 Professor Lee Carkner Lecture 18

2. PAL #17 Magnetic Field  Direction electron is fired into magnetic field that points north if it is deflected up  Force equation: F = qvB sin     = sin -1 [(1.7X10 -14 )/((1.6X10 -19 )(3X10 5 )(0.5))]   =  v vector points 45 west of north, which is pointed northwest, so electron was fired from southeast

3. Electron in B Field v B  North West South East From right hand rule: B is north and force is up so v is from west (reversed to east for electron)

4. A beam of electrons is pointing right at you. What direction would a magnetic field have to have to produce the maximum deflection in the right direction? A)Right B)Left C)Up D)Down E)Right at you

5. A beam of electrons is pointing right at you. What direction would a magnetic field have to have to produce the maximum deflection in the up direction? A)Right B)Left C)Up D)Down E)Right at you

6. A beam of electrons is pointing right at you. What direction would a magnetic field have to have to produce no deflection? A)Right B)Left C)Up D)Down E)Right at you

7. Electric and Magnetic Force  How do the electric and magnetic forces differ?  Dependences   Magnetic force depends on v and , as well as B and q  Vector   Force vector does change for a magnetic field, since as the particle is deflected the v vector changes 

8. Particle Motion  A particle moving freely in a magnetic field will have one of three paths, depending on   Straight line   Circle   Helix   This assumes a uniform field that the particle does not escape from

9. Circular Motion

10.  If the particle moves at right angles to the field the force vector will cause the path to bend   The particle will move in a circle  How big is the circle?  Magnetic force is F =  Centripetal force is F =  We can combine to get r = mv/qB  Radius of orbit of charged particle in a uniform magnetic field

11. Circle Properties  Circle radius is inversely proportional to q and B   r is directly proportional to v and m   Can use this idea to make mass spectrometer   Send mixed atoms through the B field they will come out separated by mass

12. Today’s PAL  How long would it take an electron to complete one circular orbit around a 1 G magnetic field?

13. Helical Motion  If the initial velocity is not completely perpendicular to the field, instead of a circle you get a spiral or helix  Charged particles will spiral around magnetic field lines   For example, if the lines begin and end at a pole   Examples:   Gyrosynchrotron radio emission from planets and stars

14. Helical Motion

15. Solar Wind Particles in Earth’s Magnetic Field

16. Magnetic Field and Current  Since a current is moving charge, a magnet will produce a force on a wire with a current flowing through it   So qv = IL, thus: F = BIL sin    We can use the right hand rule to get the direction of the force  Use the direction of the current instead of v

17. Force on a Wire

18. Force on a Loop of Wire   Consider a loop of wire placed so that it is lined up with a magnetic field   Two sides will have forces at right angles to the loop, but in opposite directions  The loop will experience a torque

19. Loop of Current

20. Torque on Loop  For a loop of width w and height h, force is F = BIL sin  for each long side  Since  = 90 and L = h,  The torque is the force times the moment arm (distance to the center), which is w/2  Total torque =  but hw is the area of the loop, A   If the field is at angle  to the loop then 

21. Torque on Loop

22. General Loops  If there are multiple loops (N), the torque is the sum of each  = IBAN sin    A loop placed along a magnetic field will try to align such that the field goes straight through it   Can harness the spin to do work  Called a motor

23. Next Time  Read 20.7-20.8  Homework: Ch 20, P 4, 17, 38, 49  Exam #2 Friday