Magnetic Force

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 q • q = sin-1 [(1.7X10-14)/((1.6X10-19)(3X105)(0.5))] • q = • v vector points 45 west of north, which is pointed northwest, so electron was fired from southeast

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

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? • Right • Left • Up • Down • 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? • Right • Left • Up • Down • 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? • Right • Left • Up • Down • Right at you

7. Electric and Magnetic Force • How do the electric and magnetic forces differ? • Dependences • Magnetic force depends on v and q, 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 q • Straight line • Circle • Helix • This assumes a uniform field that the particle does not escape from

9. Circular Motion

10. Circular Motion • 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 q • 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 q for each long side • Since q = 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 q to the loop then

21. Torque on Loop

22. General Loops • If there are multiple loops (N), the torque is the sum of each t = IBAN sin q • 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