**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

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
**

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

* Can humans sense magnetic fields? No.