EMEC - Greg: Difference between revisions

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=Definitions=
=Definitions=


{|class="wikitable"
{| class="wikitable" border="1"
| Symbol || Units || Name
! Symbol !! Units !! Name
|-
|-
| <math>\overrightarrow{E}</math>|| <math>\frac{V}{M}</math> || Electric Field Intensity
| <math>\overrightarrow{E}</math>|| <math>\frac{V}{M}</math> || Electric Field Intensity
Line 15: Line 15:
=Analogies between Electric & Magnetic Circuits=
=Analogies between Electric & Magnetic Circuits=


{|border="1"
 
| Electric || Magnetic
 
|-
{|class="wikitable" border="1"
| <math>V = \int \overrightarrow{E} \cdot \overrightarrow{dl}</math>|| <math>\overrightarrow{F} = \int \overrightarrow{H} \cdot \overrightarrow{dl}</math>
! Electric !!  Magnetic !! Notes
|-
|-
| <math>\sum_{n} V_{n} = 0 = \oint \overrightarrow{E} \cdot \overrightarrow{dl}</math> Kirchoff's voltage law|| <math>\oint \overrightarrow{H} \cdot \overrightarrow{dl} = N \cdot i = \sum_{n} H \cdot l + N \cdot i = 0 </math>
| <math>V = \int \overrightarrow{E} \cdot \overrightarrow{dl}</math>
| <math>\overrightarrow{F} = \int \overrightarrow{H} \cdot \overrightarrow{dl}</math>
|-
|-
| <math>\sum_{n} I_{n} = 0 = \oint_{S} \overrightarrow{J} \cdot \overrightarrow{dS}</math> Kirchoff's current law|| <math>\oint \overrightarrow{B} \cdot \overrightarrow{dS} = 0 </math> The B-field has to go around in a loop
| <math>\sum_{n} V_{n} = 0 = \oint \overrightarrow{E} \cdot \overrightarrow{dl}</math>  
| <math>\oint \overrightarrow{H} \cdot \overrightarrow{dl} = N \cdot i = \sum_{n} H \cdot l + N \cdot i = 0 </math>
|Kirchoff's voltage law
|-
|-
| <math>\oint \overrightarrow{J} \cdot \overrightarrow{dS} = I</math> || <math>\int \overrightarrow{B} \cdot \overrightarrow{dS} = \overbrace{\Phi}^{phi} </math> Magnetic flux
| <math>\sum_{n} I_{n} = 0 = \oint_{S} \overrightarrow{J} \cdot \overrightarrow{dS}</math>  
| <math>\oint \overrightarrow{B} \cdot \overrightarrow{dS} = 0 </math>
|Kirchoff's current law, The B-field has to go around in a loop
|-
|-
| <math> R = \frac{V}{I}</math> || <math> \overbrace{R}^{reluctance} = \frac{F}{\Phi} = \frac{N \cdot i}{\Phi}</math>
| <math>\oint \overrightarrow{J} \cdot \overrightarrow{dS} = I</math>  
|-
| <math>\int \overrightarrow{B} \cdot \overrightarrow{dS} = \overbrace{\Phi}^{phi} </math>
| <math> I = \frac{V}{R} = G \cdot V </math> or <math>\overrightarrow{J} = \sigma \cdot \overrightarrow{E}</math> || <math>\overrightarrow{B} = \mu \cdot H </math> assumed linearity (though it's not always the case - think hysteresis loop
|Magnetic flux
|}
 
 
=== Parenthesizing big expressions, brackets, bars ===
{| class="wikitable"
! Feature !! Syntax !! How it looks rendered
|-
|-
| Bad
| <math> R = \frac{V}{I}</math>  
| <code>( \frac{1}{2} )</code>
| <math> \overbrace{R}^{reluctance} = \frac{F}{\Phi} = \frac{N \cdot i}{\Phi}</math>
| <math>( \frac{1}{2} )</math>
|-
|-
| Good
| <math> I = \frac{V}{R} = G \cdot V </math> or <math>\overrightarrow{J} = \sigma \cdot \overrightarrow{E}</math>
| <code>\left ( \frac{1}{2} \right )</code>
| <math>\overrightarrow{B} = \mu \cdot H </math>
| <math>\left ( \frac{1}{2} \right )</math>
| Assumes linearity - exceptions: Hysterisis loop, etc
|}
|}

Revision as of 12:27, 7 January 2010

Definitions

Symbol Units Name
E VM Electric Field Intensity
D CM2 Electric Flux Density
H AM Magnetic Field Intensity
B T=WM2 Magnetic Flux Density

Analogies between Electric & Magnetic Circuits

Electric Magnetic Notes
V=Edl F=Hdl
nVn=0=Edl Hdl=Ni=nHl+Ni=0 Kirchoff's voltage law
nIn=0=SJdS BdS=0 Kirchoff's current law, The B-field has to go around in a loop
JdS=I BdS=Φphi Magnetic flux
R=VI Rreluctance=FΦ=NiΦ
I=VR=GV or J=σE B=μH Assumes linearity - exceptions: Hysterisis loop, etc