W06D2 Magnetic Forces and Sources of Magnetic Fields

1. W06D2 Magnetic Forces and Sources of Magnetic Fields W06D2 Magnetic Force on Current Carrying Wire, Sources of Magnetic Fields: Biot-Savart Law Reading Course Notes: Sections 8.3, 9.1-9.2

2. Review Week 6 Tuesday from 9-11 pm in 26-152 PS 6 due Week 6 Tuesday at 9 pm in boxes outside 32-082 or 26-152 W06D3 PS05: Calculating Magnetic Fields and Magnetic Force Reading Course Notes: Sections 8.9, 8.10, 9.10.1, 9.11.1-.3, 9.11.7-.8 Exam 2 Thursday March 21 7:30 - 9:30 pm Conflict Exam 2 March 22 9-11 am or 10-12 noon Announcements

3. Outline Magnetic Force on Current Carrying Wire Sources of Magnetic Fields Biot-Savart Law

4. Magnetic Force on Current-Carrying Wire Current is moving charges, and we know that moving charges feel a force in a magnetic field

5. Magnetic Force on Current-Carrying Wire

6. Magnetic Force on Current-Carrying Wire If the wire is a uniform magnetic field then If the wire is also straight then

7. Demonstration:Wire in a Magnetic Field (Jumping Wire) G8 http://tsgphysics.mit.edu/front/?page=demo.php&letnum=G%208&show=0

8. Demonstration:Series or Parallel Current Carrying Wires G9 http://tsgphysics.mit.edu/front/?page=demo.php&letnum=G%209&show=0 You tube video of experiment showing parallel wires attracting http://youtu.be/rU7QOukFjTo or repelling: http://youtu.be/bnbKdbXofEI

9. Group Problem: Current Loop A conducting rod of uniform mass per length l is suspended by two flexible wires in a uniform magnetic field of magnitude B which points out of the page and a uniform gravitational field of magnitude g pointing down. If the tension in the wires is zero, what is the magnitude and direction of the current in the rod?

10. Sources of Magnetic Fields

11. What Creates Magnetic Fields: Moving Charges http://youtu.be/JmqX1GrMYnU

12. Electric Field Of Point Charge An electric charge produces an electric field: : unit vector directed from the charged object to the field point P

13. Magnetic Field Of Moving Charge Moving charge with velocity v produces magnetic field: P unit vector directed from charged object to P permeability of free space

14. Currents are Sources of Magnetic Field

15. Demonstration:Field Generated by Wire G12 http://tsgphysics.mit.edu/front/?page=demo.php&letnum=G%2012&show=0

16. Continuous Moving Charge Distributions:Currents & Biot-Savart

17. From Charges to Currents?

18. The Biot-Savart Law Current element of length ds pointing in direction of current I produces a magnetic field: http://web.mit.edu/viz/EM/visualizations/magnetostatics/MagneticFieldConfigurations/CurrentElement3d/CurrentElement.htm

19. The Right-Hand Rule #2

20. Concept Question: Biot-Savart The magnetic field at P points towards the • +x direction • +y direction • +z direction • -x direction • -y direction • -z direction • Field is zero

21. Concept Question Answer: Biot-Savart Answer: 6. is in the negative z direction (into page) The vertical line segment contributes nothing to the field at P (it is parallel to the displacement). The horizontal segment makes a field pointing into the page by the right-hand rule # 2 (right thumb in direction of current, fingers curl into page at P.

22. Concept Question: Bent Wire The magnetic field at P is equal to the field of: • a semicircle • a semicircle plus the field of a long straight wire • a semicircle minus the field of a long straight wire • none of the above

23. Concept Question Answer: Bent Wire Answer: 2. Semicircle + infinite wire All of the wire makes into the page. The two straight parts, if put together, would make an infinite wire. The semicircle is added to this to get the magnetic field

24. Repeat Demonstration:Parallel & Anti-Parallel Currents G9 http://tsgphysics.mit.edu/front/?page=demo.php&letnum=G%209&show=0

25. Concept Question: Parallel Wires Consider two parallel current carrying wires. With the currents running in the opposite direction, the wires are • attracted (opposites attract?) • repelled (opposites repel?) • pushed another direction • not pushed – no net force • I don’t know

26. Concept Q. Answer: Parallel Wires Answer: 1. The wires are repelled I1 creates a magnetic field into the page at wire 2. That makes a force on wire 2 to the right. I2 creates a magnetic field into the page at wire 1. That makes a force on wire 1 to the left.

27. Can we understand why? Whether they attract or repel can be seen in the shape of the created B field http://youtu.be/5nKQjKgS9z0 http://youtu.be/nQX-BM3GCv4 You tube videos of field line animations showing why showing parallel wires attract: or repel:

28. Concept Question: Current Carrying Coils • parallel currents that attract • parallel currents that repel • opposite currents that attract • opposite currents that repel The above coils have

29. Concept Q. Answer: Current Carrying Coils Look at the field lines at the edge between the coils. They are jammed in, want to push out. Also, must be in opposite directions Answer: 4. Opposite currents that repel http://web.mit.edu/viz/EM/visualizations/magnetostatics/ForceOnCurrents/MagneticForceRepel/MagneticForceRepel.htm

30. Example : Coil of Radius R Consider a coil with radius R and current I Find the magnetic field B at the center (P)

31. Example : Coil of Radius R Consider a coil with radius R and current I • 1) Think about it: • Legs contribute nothing • I parallel to r • Ring makes field into page • 2) Choose a ds • 3) Pick your coordinates • 4) Write Biot-Savart

32. Animation: Magnetic Field Generated by a Current Loop http://web.mit.edu/viz/EM/visualizations/magnetostatics/calculatingMagneticFields/RingMagInt/RingMagIntegration.htm

33. Example: Coil of Radius R In the circular part of the coil… Biot-Savart:

34. Example : Coil of Radius R Consider a coil with radius R and current I direction into page

35. Group Problem:B Field from Coil of Radius R Consider a coil with radius R and carrying a current I WARNING: This is much harder than the previous problem. Why?? What is B at point P?