Physics 2

1. Chapter 19 Sections 4-7 Physics 2

2. Diamagnetic – atoms have no magnetic moments - under influence of B field the motion of electrons in the atoms change to oppose field ex – bismuth, lead, graphite, quartz, glass Types of Magnetic Materials

3. Paramagnetic – atoms have magnetic moments that are independent of each other - under influence of B field the motion of electrons in atoms changes to align with field - net effect is small overall magnetization in direction of B field - magnetization disappears when field is removed ex – aluminum, platinum, sodium Types of Magnetic Materials

4. Ferromagnetic – atoms have magnetic moments that aren’t independent of each other (domains) - under influence of B field the domains either rotate to align with field or domains that are in alignment grow - net effect depends on strength of B field - magnetization remains when field is removed ex – iron, cobalt, nickel Types of Magnetic Materials

5. F = I l B sinΘ where I – current l – length of wire B – magnetic field Θ – angle between I and B Note: F max when wire is perpendicular to B F = 0 when wire is parallel to B Force on Current –Carrying Wire

6. Right Hand Rule #3 Point fingers of right hand in direction of current, bend fingers in the direction of B, thumb points in direction of force on current –carrying wire Force on Current –Carrying Wire

7. Sample Problem The figure shows a wire in the magnetic field of a permanent magnet. The field has a nearly uniform magnitude over a region of 6 cm and is approximately zero elsewhere. Find the magnetic force on the wire which carries a current of 40 A. The wire is perpendicular to the field and B = .5 T. N I S N I S

8. Sample Problem The voice coil of a speaker has a diameter of 2.5 cm, contains 55 turns of wire, and is placed in a 0.1 T B field. The current in the voice coil is 2 A. Determine the magnetic force that acts on the coil and cone. If the voice coil and cone have a combined mass of 0.02 kg, find their acceleration.

9. Torque on Current Loop I Τ = IAB sinφ where I – current A – area of a loop B – magnetic field φ – angle between normal to plane and B N S

10. Torque on Current Loop If loop has N turns Τ =NIAB sinφ where I – current A – area of a loop B – magnetic field φ – angle between normal to plane and B Note: T is max when plane of loop is along B T is 0 when plane of loop is perpendicular to B

11. In the equation Τ =NIAB sinφ NIA = m and is called the magnetic moment Direction is perpendicular to the plane of the loop Magnetic Moment

12. Sample Problem A coil of wire has an area of 2 x 10-4 m2, consists of 100 loops, and contains a current of 45 mA. The coil is placed in a uniform B field of 0.15 T. Determine the magnetic moment of the coil. Find the maximum torque that the B field can exert.

13. B = μoI / 2Πr μo - permeability of free space = 4Π x 10-7 Tm/A I – current R – distance from wire B Field on a Current Carrying Wire

14. Sample Problem A long straight wire is directed perpendicular to the page and carries a current of 100 A into the page. Find the magnetic field at a field point 4 cm to the right of the wire.

15. Current carrying wires produce B fields B fields exert forces on current carrying wires One wire can exert a force on another wire B Field on a Current Carrying Wire

16. Sample Problem Two parallel straight wires are separated by a distance of 0.065 m and carry currents of I1 = 15 A and I2 = 7 A. Find the magnitude and direction of the force that the B field of wire 1 applies to a 1.5 m length of wire 2 when the currents are (a) in the same direction and (b) in the opposite direction.

17. F2 = ( μoI1I2l ) / ( 2Πr) If wires carry current in the same direction they attract If wires carry current in opposite directions they repel B Field on a Current Carrying Wire

18. Sample Problem Two long straight parallel wires 1 cm apart each carry a current of 1 A in the same direction. Find the magnitude of the force on a 1 m length of either wire.

19. I Take a wire a bend it into a loop B field is into the center of the loop B = μo I / 2R where μo = 4Π x 10-7 Tm/A I – current R – radius of loop B field on a Wire Loop

20. Sample Problem Find the B field at the center of a circular loop of radius 2 cm, carrying a current of 10 A clockwise.

21. I Often the loop is several turns of wire that are bound together to make a flat coil All the loops produce B fields that point in the same direction inside the coil so the B field looks a lot like a bar magnet B = Nμo I / 2R B Field on Wire Loops

22. Sample Problem A long straight wire carries a current of 8 A. A portion of the wire is then bent into a circular loop of radius 0.02 m. Find the magnitude and direction of the net B field at the center of the loop. I

23. Solenoid • Long coil of wire wound in the shape of a helix • If wound so its length is large compared to the diameter then the B field is practically uniform down its length

24. Solenoid • B for the interior of a solenoid B = μo n I where n – number of turns/length I - current

25. Solenoid • Solenoids are sometimes called electromagnets and have advantages over permanent magnets - strength can be altered by changing I or the number of turns/length - can easily switch NS poles by reversing current