4 jan 2010
L i m i t A → ∞ : {\displaystyle Limit\ A\ \to \infty :}
X 0 = 1 β X s ⇒ V 0 = R 1 + R 2 R 1 V i n {\displaystyle X_{0}\ ={\frac {1}{\beta }}X_{s}\ \Rightarrow V_{0}={\frac {R_{1}+R_{2}}{R_{1}}}V_{in}}
X i = 0 {\displaystyle X_{i}\ =0}
Picture drawn by Kirk Betz based on drawing by Dr. Frohnes, lecture Jan. 4, 2010
V i n = V 0 ( R 1 R 1 + R 2 ) {\displaystyle V_{in}\ =V_{0}({\frac {R_{1}}{R_{1}+R_{2}}})} .
V 0 = 1 ( R 1 R 1 + R 2 ) V i n {\displaystyle V_{0}\ ={\frac {1}{({\frac {R_{1}}{R_{1}+R_{2}}})}}V_{in}}
jan 6 2010
F → = q v → × B → {\displaystyle {\vec {F}}\ =q{\vec {v}}\times {\vec {B}}}
d F → = I d l → × B → {\displaystyle d{\vec {F}}\ =Id{\vec {l}}\times {\vec {B}}}
F = H l 1 + H l 2 {\displaystyle {\mathcal {F}}=Hl_{1}+Hl_{2}}
V = R 1 I + R 2 I {\displaystyle V\ =R_{1}I+R_{2}I}
Picture drawn by Kirk Betz based on drawing by Dr. Frohnes, lecture Jan. 6, 2010
∫ H → d l → = F {\displaystyle \int {\vec {H}}d{\vec {l}}={\mathcal {F}}}
∮ H → d l → = N i = ∑ n H l + N i = 0 {\displaystyle \oint {\vec {H}}d{\vec {l}}=Ni=\sum _{n}Hl+Ni=0}
∮ B → d s → = 0 {\displaystyle \oint {\vec {B}}d{\vec {s}}=0}
∫ B → d s → = ϕ ≈ B A r e a M a g n e t i c F l u x {\displaystyle \int {\vec {B}}d{\vec {s}}=\phi \thickapprox BA_{rea}\ Magnetic\ Flux}
R ≡ R e l u c t a n c e F ϕ = N i ϕ {\displaystyle {\mathcal {R}}\equiv Reluctance\ {\frac {\mathcal {F}}{\phi }}={\frac {Ni}{\phi }}}
B → = μ H → A s s u m e s L i n e a r i t y {\displaystyle {\vec {B}}=\mu {\vec {H}}\ Assumes\ Linearity}
R l μ A {\displaystyle {\mathcal {R}}{\frac {l}{\mu A}}}
B H field histogram pic
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