1. Magnetism CHAPTER 29 : Magnetic fields exert a force on moving charges. CHAPTER 30 : Moving charges (currents) create magnetic fields. CHAPTERS 31, 32: Changing magnetic fields create electric fields. (Induction)

2. Magnetic fields Magnetic poles, forces, and fields Force on a moving charged particle Force on a current-carrying wire

3. Magnets and Magnetic Forces Similar model to electrostatics: Each magnet has two poles at its ends. B is the magnetic field vector (magnetic flux density) NS Magnetic poles come in two types, “N” and “S”. Due to the Earth’s magnetism, a magnet will tend to rotate until the “N” end points North. (the earth’s north magnetic pole is actually a south pole) Forces between magnets are due to the forces between each pair of poles, similar to the electrostatic forces between point charges.

4. NN S S S N like poles repel NN unlike poles attract The force gets smaller as distance increases.

5. N N S Magnetic Field B Magnetic poles produce a field B (think of S as a – charge and of N as a + charge) S The external field exerts forces on poles B B F F

6. NS Quiz What is the direction of the force on a magnetic dipole placed in a uniform magnetic field? B

7. Magnetic field lines and Magnetic Dipoles Compass needle (a magnetic dipole) aligns with B S N NSNS compass Lines point out from N pole B B

8. Electric charge and Magnetic fields Hans Ørsted discovered (1819) that moving electric charges create magnetic fields. Also, external magnetic fields exert forces on moving electric charges. A current loop acts like a magnetic dipole.

9. Define B by the force that an external field exerts on a moving charge: Charge q moving with velocity, feels a force (vector product) + q B v F

10. 1) 2)  NO work done! 3) 4) For a negative charge, the force is in the opposite direction. UNITS: Also… 1 Gauss (G) = 10 -4 T

11. Typical Fields Earth’s Field~ 1 x 10 -4 T (1 Gauss) Strong fridge magnet~ 10 -2 T (100 G) Big lab electromagnet~ 4 T (40,000 G) Superconducting magnet up to ~ 20 T (200,000 G)

12. Vector Diagrams X into the page (tail feathers of arrow) out of the page (point of arrow) For vectors perpendicular to the page, we use: The three vectors F, v, B never lie in a single plane, so the diagrams are always three-dimensional. The following convention helps with drawing the vectors.

13. Examples For a positive charge q moving with velocity v: draw the force vector. x x x x x x x x v B B v v B v B x

14. + + + + + + + B current I Current I flows from left to right. In what direction is the force on the wire? L Wire

15. + + + + + + + B The total force on the wire of length L is F = Nqv x B, where N is the number of charges in length L. N = (number of charges/volume) x (volume) = n x (AL), where A is the cross-sectional area So, F = (nALqv) x B = (nqvA)L x B F = I L x B or, (straight wire, uniform B ) The vector length L points along the wire in the direction of the current.

16. Example Assume the earth’s magnetic field is 0.5 x 10 -4 T, and points North, 50 o below the horizontal. What is the force (magnitude and direction) on a straight horizontal power line 100 m long, carrying 400 A: 50 o 0.5 x 10 -4 T A)if the current is flowing North B)if the current is flowing East up north

17. Solution