2. As You Come In… What is the direction of the magnetic field acting on wire 1 from wire 2? Does it apply a force to wire 1? I1I1 x y I2I2 z

3. A Week of Laws Lots of very smart people, so little time! Many scientists made observations about magnetism (and electricity) Some derived equations—others, patterns in behavior The list: Biot-Savart Law Ampere’s Law Lenz’s Law Faraday’s Law

4. Finding Magnetic Fields Ideal goal: find magnetic field, anywhere, for any current source Challenge accepted by: Jean-Baptiste Biot Félix Savart

5. Finding Magnetic Fields Images obtained from: http://en.wikipedia.org/wiki/Jean-Baptiste_Biot#mediaviewer/File:Jean_baptiste_biot.jpg, and http://cdn.timerime.com/cdn-4/upload/resized/124038/1379226/resized_image2_ebcb59e0639d0abe2ed28df58dc03baf.jpg Jean-Baptiste Biot Félix Savart CENSORED? ?

6. Finding Magnetic Fields Images obtained from: http://en.wikipedia.org/wiki/Jean-Baptiste_Biot#mediaviewer/File:Jean_baptiste_biot.jpg, and http://cdn.timerime.com/cdn-4/upload/resized/124038/1379226/resized_image2_ebcb59e0639d0abe2ed28df58dc03baf.jpg Jean-Baptiste Biot Félix Savart

7. Using Biot-Savart’s Law Suppose you have an infinitely long wire with current I Want to know B at a location that is a distance x from wire x B? x y z I location

8. Using Biot-Savart’s Law Magnitude of current constant throughout wire Take a portion of wire of length d l —has direction of current This wire portion is a distance r from location—varies with changing d l δ: angle between d l and r x B? x y z I location dldl r δ

9. Using Biot-Savart’s Law x B? x y z I location dldl r δ +∞ -∞ +∞ -∞ +∞ -∞

10. Using Biot-Savart’s Law x B? x y z I location dldl r δ l +∞ -∞ +∞ -∞

11. Using Biot-Savart’s Law x B? x y z I location dldl r δ l +∞ -∞ Integral table obtained from: http://integral-table.com/downloads/integral-table.pdf

12. Using Biot-Savart’s Law x B? x y z I location dldl r δ l

13. Using Biot-Savart’s Law x B? x y z I location dldl r δ l

14. Using Biot-Savart’s Law x B? x y z I location dldl r δ l

15. Using Biot-Savart’s Law x B? x y z I location dldl r δ l

16. Using Biot-Savart’s Law x B? x y z I location dldl r δ l

17. For Tuesday… New law tomorrow: get ready for more math Brush up on your torque knowledge… Image obtained from: http://www.astro.cz/_data/images/news/2013/09/27/pe_78b.jpg André-Marie Ampère