Inductors and Faraday's Law

We start by contemplating magnetism: there are two sources for magnetism. Ferromagnetic materials and current flowing through a wire, particularly in the shape of a solenoid. And the current can be of two sorts: AC or DC. Below shows the equation that allows you to compute the B field based on current flowing through, a wire, and the wire's geomety (path through 3D space).


where μ0 = 4*π*10^-7 H
sdsu-physics.org

From the cross product above image: What do the B fields lines look like due to current in a straight wire? due to current in a wire going in a loop, or a helix? From a more mathematical point of view, note that B fields have a non-zero curl.

Faraday's Law

Our 3 Ohm's Law type equations are now
V = I * R
Q = C * V
φ = L * I where L is inductance, measured in Henrys.

Differentiate the last equation to come up with flux = phi = L * i(t)==> v(t)= L di(t)/dt ==> V(s) = s*L*I(s)-i(0)

The unit of inductance is the Henry.

Consider self inductance L of a single coil, and mutual inductance M (between 2 coils, such as in a transformer).

Griffiths p. 295:

what about minus sign in Faraday's Law? from Griffiths:
"Inductance (like capacitance) is an intrinsically positive quantity. Lenz's Law, which is enforced by the minus sign, dictates that the EMF (voltage) is in such a direction as to oppose any change in current. For this reason, it is called a back EMF. Whenever you try to alter the current in a wire you must fight againt this back EMF. Thus inductance plays somewhat the same role in electric circuits that mass plays in mechanical systems: The greater L is, the harder it is to change the current, just as the larger the mass, the harder it is to change an object's velocity."

Inductors in series add, in parallel they are summed like resistors in parallel: 1/LT = 1/L1 + 1/L2 + 1/L3 + ...

Fabrication of coils with enameled magnet wire:

Energy: An ideal inductor doesn't dissipate energy, it stores energy; in the case of an inductor,
faculty.wwu.edu

How a transformer works: primary, secondary windings
Vout =(num_sec_wind/num_pri_wind)*Vin... Vin muct be AC--> sinusoidals...
The primary and secondary windings are related by their mutual inductance, M.

How transformers work: http://www.scienceaid.co.uk/physics/electricity/electromagnetism.html

Demo solenoid:
moving an iron piston with electrically-induced magnetic field B

Power supply = transformer + rectifier + LP filter + regulator
Demo of E3631A limiting current and voltage with 4.7 ohm resistor
on 25v supply. resistance of jumpers! 2 ohms...

How a switching power supply works to have no loss at the regulator.

The role of an inductor in a defibrillator. Second order system, overdamped please.

Lorentz force Law

will help explain how an electric motor armature rotates...

Other "magnetic" examples:
* Magnetoencephalography = MEG vs EEG
* Magnetic drug delivery
* Isolation transformers
* magnetically controlled shunts for hydrocephalus

*
birds navigating during migration over open ocean on a cloudy night...Alaska to New Zealand...
* Can humans sense magnetic fields? No.