From d8241c18decdbed0d5a818db8e5d7398f4ae463d Mon Sep 17 00:00:00 2001
From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Mon, 18 Jun 2018 16:53:56 +1000
Subject: [PATCH] add to fields notes

---
 physics/fields2.md | 99 +++++++++++++++++++++++++++++++++++++++-------
 1 file changed, 84 insertions(+), 15 deletions(-)

diff --git a/physics/fields2.md b/physics/fields2.md
index c4ec99a..4b5439a 100644
--- a/physics/fields2.md
+++ b/physics/fields2.md
@@ -3,8 +3,10 @@
 Non-contact forces:
 - strong nuclear force
 - weak nuclear force
-- electromagnetic force (dipoles)
-- gravitational force (monopoles)
+- electromagnetic force
+- - electric fields (dipoles & monopoles)
+- - magnetic fields (dipoles only)
+- gravitational force (monopoles only)
 
 ---
 
@@ -45,6 +47,7 @@ Characteristics of gravitational fields:
 - monopoles
 - attractive force
 - extends to infinite distance, but diminishes with inverse square law
+- charge produced by gravity = $GM$
 
 ### Work in a gravitational field
 
@@ -56,9 +59,17 @@ Area under field-distance graph = $\Delta E_g / \operatorname{kg}$
 
 ### Satellites
 
-## Electromagnetism
+## Magnetic fields
 
-### Electric fields
+### Characteristics
+- field lines always go from N -> S
+- dot means out of page, cross means into page
+- ${E_1 \over E_2}={r_1 \over r_2}^2$
+
+
+## Electric fields
+
+### Characterisics
 
 - surrounds +ve and -ve charges
 - exerts force on other changes in its field
@@ -67,13 +78,13 @@ Area under field-distance graph = $\Delta E_g / \operatorname{kg}$
 - can be constrained to a fixed distance (conductors / insulators)
 - current flows from +ve to -ve
 
-#### Field lines
+### Field lines
 - +ve to -ve
 - start and end $\perp$ to surface
 - field lines never cross
 - point charges - radiate from centre
 
-#### Forces
+### Forces
 
 $$F=qE$$
 
@@ -82,7 +93,7 @@ $F$ is the force on charged particle
 $q$ is the charge of object experiencing force (Coulombs)
 $E$ is the strength of the electric field (Newtons / Coloumb or Volts / metre)
 
-#### Work in electric fields
+### Work in electric fields
 
 $$W=qV$$
 
@@ -91,7 +102,7 @@ $W$ is the work done on +ve point charge or in field
 $q$ is the charge of point charge being acted on
 $V$ is the potential (voltage) between points
 
-#### Coulomb's law
+### Coulomb's law
 
 
 $$F=k{{q_1q_2}\over r^2}$$
@@ -101,26 +112,25 @@ $k$ is Coulomb's constant $9.0 \times 10^9 \operatorname{N m^2 C^{-2}}$
 $q_1$ and $q_2$ are the charges on the interacting points
 
 
-#### Electric field at distance from a charge
+### Electric field at distance from a charge
 
 $$E=k{Q \over r^2}$$
 
-### Electromagnetism
-
-#### Lenz's law
+### Lenz's law
 - Right hand grip rule (relationship between directions of $I, F$)
+- Eddy currents counter movement within a field
 
-#### Solenoids
+### Solenoids
 - Coil around core (like a transformer but field is transferred to kinetic energy)
 
-#### Magnetic force on charged particles
+### Magnetic force on charged particles
 
 $$F=qvB$$
 
 where
 $v$ is the component of velocity which is $\perp$ to magnetic field
 
-#### Right hand slap rule
+### Right hand slap rule
 
 
 **Field, current and force are all 90 degree to each other**
@@ -135,6 +145,65 @@ force
 
 Force is given by $F=nBIl$
 
+
+### Faraday's law of induction
+
+$$\epsilon = -N{{\Delta \Phi_B}\over{\Delta t}}$$
+
+where
+$\epsilon$ is induced EMF (voltage)
+$N$ is the number of turns in the primary coil
+$\Phi_B$ is the magnetic flux (Wb or V / s)
+$\Delta t$ is the change in time for one cycle (can be derived from period or frequency)
+
+### Flux through coils
+$$\Phi_B = B_{\perp}A$$
+
+where
+$B_\perp$ is the field strength (Tesla)
+$A$ is the area of the field perpendicular to field lines
+
+if $B {\not \perp} A, \Phi_B \rightarrow 0$
+if $B \parallel A, \Phi_B = 0$
+
+- flux-time graphs ($t$ on $x$-axis): $\operatorname{gradient} \times n = \operatorname{emf}$
+
+
+**EMF is proportionate to change in flux**
+
+**Induced EMF opposes (counters) change in flux**
+
+### Transformer equation
+
+$${V_p \over V_s}={N_p \over N_s}$$
+$${I_p \over I_s}={N_s \over N_p}$$
+
+- core strengthens and "focuses" ac flux $\Phi$ through secondary coil
+
+
+### Root mean square
+
+$$V_{\operatorname{rms}} = {V_{\operatorname{p\rightarrow p}} \over \sqrt{2}}$$
+
+## Power transmission
+- 240 V / 50 Hz in Australia
+- higher voltages have lower $V_{\operatorname{loss}}$
+- ac is used because its voltage is easily changed with xfmrs
+
+### Safety
+- $\ge 30 \operatorname{mA}$ through heart is dangerous
+
+### Transmission $P_{\operatorname{loss}}$
+
+$$P_{\operatorname{loss}} = \Delta V I = I^2 R = {{\Delta V^2} \over R}$$
+
+where
+$R$ is the total resistance (derived from resistance per distance)
+
+To reduce power loss, use lower resistance (thicker) wires or increase voltage / reduce current with transformers
+
+
+
 ### Motors
 
 #### DC
-- 
2.43.2