Magnetism (3 weeks)

1. Magnetism (3 weeks) 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. S N Magnets and Magnetic Forces Similar model to electrostatics: Each magnet has two polesat its ends.Bis the magnetic field vector (magnetic flux density) 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. N N S S N N N S unlike poles attract like poles repel The force gets smaller as distance increases.

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

6. S N 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 B B compass N S SN Lines point out from N pole

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) F B q + v

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 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. For vectors perpendicular to the page, we use: X into the page (tail feathers of arrow) out of the page (point of arrow)

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

14. + + + + + + + B Wire current I L Current I flows from left to right. In what direction is the force on the 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 (straight wire, uniform B) or, The vector length L points along the wire in the direction of the current.

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

17. Solution