1. Physics for Scientists and Engineers II, Summer Semester 2009 1 Lecture 17: July 1 st 2009 Physics for Scientists and Engineers II

2. Physics for Scientists and Engineers II, Summer Semester 2009 2 Example (32.1 in book): Inductance of a Solenoid

3. Physics for Scientists and Engineers II, Summer Semester 2009 3 Energy in a Magnetic Field + - power provided by battery power dissipated in resistor (heat) Energy stored in the inductor per unit time (rate of energy storage)

4. Physics for Scientists and Engineers II, Summer Semester 2009 4 Energy in a Magnetic Field Additional energy stored in the magnetic field of the inductor per unit time (rate of energy storage). Note: While the current increases (dI/dt > 0), amount of energy in the inductor increases. Once the maximum current is reached: dI/dt=0 and the energy in the inductor no longer increases (it has then reached it’s maximum).

5. Physics for Scientists and Engineers II, Summer Semester 2009 5 Energy density of a Magnetic Field

6. Physics for Scientists and Engineers II, Summer Semester 2009 6 Mutual Inductance Coil 1 with N 1 turns Coil 2 with N 2 turns

7. Physics for Scientists and Engineers II, Summer Semester 2009 7 Mutual Inductance

8. Physics for Scientists and Engineers II, Summer Semester 2009 8 Example: Mutual Inductance between two long wire loops exactly on top of each other.

9. Physics for Scientists and Engineers II, Summer Semester 2009 9 Example: Mutual Inductance between two long wire loops exactly on top of each other.

10. Physics for Scientists and Engineers II, Summer Semester 2009 10 Example: Create several winding on each loop

11. Physics for Scientists and Engineers II, Summer Semester 2009 11 Oscillation in an LC Circuit + -

12. Physics for Scientists and Engineers II, Summer Semester 2009 12 Use Kirchhoff’s loop rule + - loop

13. Physics for Scientists and Engineers II, Summer Semester 2009 13 Try this solution

14. Physics for Scientists and Engineers II, Summer Semester 2009 14 Plug it into the differential equation

15. Physics for Scientists and Engineers II, Summer Semester 2009 15 Initial Conditions

16. Physics for Scientists and Engineers II, Summer Semester 2009 16 Plotting Q(t) and I(t)

17. Physics for Scientists and Engineers II, Summer Semester 2009 17 Energy in the system

18. Physics for Scientists and Engineers II, Summer Semester 2009 18 Energy in the system

19. Physics for Scientists and Engineers II, Summer Semester 2009 19 RLC Circuits (more realistic)

20. Physics for Scientists and Engineers II, Summer Semester 2009 20 Kirchhoff’s loop

21. Physics for Scientists and Engineers II, Summer Semester 2009 21 Kirchhoff’s loop

22. Physics for Scientists and Engineers II, Summer Semester 2009 22 Plug Trial Solution into Diff. Equation

23. Physics for Scientists and Engineers II, Summer Semester 2009 23 Plug Trial Solution into Diff. Equation

24. Physics for Scientists and Engineers II, Summer Semester 2009 24 Initial Condition