Physics 208: Complete Electric and Magnetic Field Essentials Ch. 27-32

1. Exam 2 covers Ch. 27-32,Lecture, Discussion, HW, Lab • Chapter 27: Electric flux & Gauss’ law • Chapter 29: Electric potential & work • Chapter 30: Electric potential & field • Chapter 28: Current & Conductivity • Chapter 31: Circuits • Chapter 32: Magnetic fields & forces • (exclude 32.6,32.8,32.10) Exam 2 is Wed. Mar. 26, 5:30-7 pm, 2103 Ch: Adam(301,310), Eli(302,311), Stephen(303,306), 180 Science Hall: Amanda(305,307), Mike(304,309), Ye(308) Physics 208, Lecture 17

2. Current Magnetic field Electric current produces magnetic field • Current (flow of electric charges )in wire produces magnetic field. • That magnetic field aligns compass needle Physics 208, Lecture 17

3. dB r dI Law of Biot-Savart B out of page • Each element of current produces a contribution to the magnetic field. r  I ds Physics 208, Lecture 17

4. Magnetic field from long straight wire:Direction y • What direction is the magnetic field from an infinitely-long straight wire? x I Physics 208, Lecture 17

5. Current dependence How does the magnitude of the B-field change if the current is doubled? y Is halved Quadruples Stays same Doubles Is quartered x I Physics 208, Lecture 17

6. Distance dependence How does the magnitude of the B-field at 2 compare to that at 1? y 2 B2=B1 B2=2B1 B2=B1/2 B2=4B1 B2=B1/4 1 x I Physics 208, Lecture 17

7. Why? • Biot-Savart says • Why B(r) 1/r instead of 1/r2 ? Small contribution from this current element. ~ independent of r Large contribution from this current element. Decreases as 1/r2 I Physics 208, Lecture 17

8. Long straight wire • All current elements produce B out of page Add them all up: r a  x Physics 208, Lecture 17

9. Forces between currents Which of these pairs of currents will attract each other? • A • A & C • B • A & B A B C Physics 208, Lecture 17

10. Force between current-carrying wires • Attractive for parallel currents. • Repulsive for antiparallel currents Physics 208, Lecture 17

11. Field from a circular loop • Each current element produce dB • All contributions add as vectors • Along axis, allcomponents cancelexcept for x-comp Physics 208, Lecture 17

12. y x z Magnetic field from loop Bz A. z Which of these graphs best represents the magnetic field on the axis of the loop? Bz B. z Bz C. z Bz D. z Physics 208, Lecture 17

13. Magnetic field from a current loop • One loop: field still loops around the wire. • Many loops: same effect Physics 208, Lecture 17

14. Solenoid electromagnet • Sequence of current loops can produce strong magnetic fields. • This is an electromagnet Physics 208, Lecture 17

15. Comparing Electric, Magnetic • Biot-Savart: calculate B-field from current distribution. • Resulting B-field is a vector, and… • complication: current (source) is a vector! • Coulomb: calculate E-field from charge distribution • Resulting E is a vector but charge (source) is not a vector Physics 208, Lecture 17

16. A shortcut: Ampere’s law • Ampere’s law • Integral around closed path proportional to current passing through any surface bounded by path. I closed path surface bounded by path • Right-hand ‘rule’: • Thumb in direction of positive current • Curled fingers show direction integration Physics 208, Lecture 17

17. ‘Testing’ Ampere’s law • Long straight wire , Br path has constant r path length = 2πr B||ds Circular path r B(r) I Surface bounded by path Physics 208, Lecture 17

18. Using Ampere’s law • Could have used Ampere’s law to calculate B path length = 2πr B constant on path B||ds Circular path r B(r) I Surface bounded by path Physics 208, Lecture 17

19. Quick Quiz • Suppose the wire has uniform current density. How does the magnetic field change inside the wire? Increases with r Decreases with r Independent of r None of the above B r Physics 208, Lecture 17

20. Building a solenoid Physics 208, Lecture 17

21. Ampere’s law for the solenoid Physics 208, Lecture 17