1. Exam 2 covers Ch. 28-33, Lecture, Discussion, HW, Lab
Exam 2 is Tue. Oct. 28, 5:30-7 pm, Ch
Chapter 28: Electric flux & Gauss’ law
Chapter 29: Electric potential & work
Chapter 30: Electric potential & field
(exclude 30.7)
Chapter 31: Current & Conductivity
Chapter 32: Circuits
(exclude 32.8)
Chapter 33: Magnetic fields & forces
(exclude 33.3, 33.6, 33.10, Hall effect)
Tue. Oct. 28, 2008
Physics 208, Lecture 17

2. Electric current produces magnetic field
Current (flow of electric charges ) in wire produces magnetic field.
That magnetic field aligns compass needle
Current
Magnetic field
Tue. Oct. 28, 2008
Physics 208, Lecture 17

3. Law of Biot-Savart
B out of page
Each element of current produces a contribution to the magnetic field. r  I ds dI dB r
Tue. Oct. 28, 2008
Physics 208, Lecture 17

4. Magnetic field from long straight wire: Directiony
What direction is the magnetic field from an infinitely-long straight wire? x I
Tue. Oct. 28, 2008
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
Tue. Oct. 28, 2008
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
Tue. Oct. 28, 2008
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
Tue. Oct. 28, 2008
Physics 208, Lecture 17

8. Long straight wire All current elements produce B out of page
Add them all up: r a  x
Tue. Oct. 28, 2008
Physics 208, Lecture 17

9. Field from a circular loop
Each current element produce dB
All contributions add as vectors
Along axis, all components cancel except for x-comp
Tue. Oct. 28, 2008
Physics 208, Lecture 17

10. Magnetic field from loopBz
Which of these graphs best represents the magnetic field on the axis of the loop? A. z Bz B. z z x y Bz C. z Bz D. z
Tue. Oct. 28, 2008
Physics 208, Lecture 17

11. Magnetic field from a current loop
One loop: field still loops around the wire.
Many loops: same effect
This is just like the elementary magnetic particle (dipole) we discussed earlier.
Tue. Oct. 28, 2008
Physics 208, Lecture 17

12. Solenoid electromagnet
Sequence of current loops can produce strong magnetic fields.
This is an electromagnet
Tue. Oct. 28, 2008
Physics 208, Lecture 17

13. 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
Tue. Oct. 28, 2008
Physics 208, Lecture 17

14. A shortcut: 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
Tue. Oct. 28, 2008
Physics 208, Lecture 17

15. Ampere’s law Sum up component of B around path
Equals current through surface.
Component of B along path I
closed path
Ampere’s law
surface bounded by path
Tue. Oct. 28, 2008
Physics 208, Lecture 17

16. ‘Testing’ Ampere’s law
Long straight wire , Br
B||ds
path has constant r
path length = 2πr
Circular path r
B(r) I
Surface bounded by path
Tue. Oct. 28, 2008
Physics 208, Lecture 17

17. Using Ampere’s law Could have used Ampere’s law to calculate B B||ds r
B constant on path
path length = 2πr
B||ds
Circular path r
B(r) I
Surface bounded by path
Tue. Oct. 28, 2008
Physics 208, Lecture 17

18. 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
Tue. Oct. 28, 2008
Physics 208, Lecture 17