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

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

Physics for Scientists and Engineers II, Summer Semester 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)

Physics for Scientists and Engineers II, Summer Semester 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).

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

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

Physics for Scientists and Engineers II, Summer Semester Mutual Inductance

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

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

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

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

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

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

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

Physics for Scientists and Engineers II, Summer Semester Initial Conditions

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

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

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

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

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

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

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

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

Physics for Scientists and Engineers II, Summer Semester Initial Condition