The Class Notes

4 jan 2010

$$\begin{gathered} Limit \\ A \\ \to \mathrm{\infty }: \end{gathered}$$

$$\begin{gathered} X_0 \\ =\frac{1}{\beta }{X}_s \\ \Rightarrow V_0=\frac{R_1+R_2}{R_1}{V}_{in} \end{gathered}$$

$$\begin{gathered} X_i \\ =0 \end{gathered}$$

Picture drawn by Kirk Betz based on drawing by Dr. Frohnes, lecture Jan. 4, 2010

$$\begin{gathered} V_{in} \\ =V_0(\frac{R_1}{R_1+R_2}) \end{gathered}$$.

$$\begin{gathered} V_0 \\ =\frac{1}{(\frac{R_1}{R_1+R_2})}{V}_{in} \end{gathered}$$

Magnetic Circuits

jan 6 2010

$$\begin{gathered} \overrightarrow{F} \\ =q\overrightarrow{v}\times \overrightarrow{B} \end{gathered}$$

$$\begin{gathered} d\overrightarrow{F} \\ =Id\overrightarrow{l}\times \overrightarrow{B} \end{gathered}$$

${ℱ}=H{l}_1+H{l}_2$

$$\begin{gathered} V \\ =R_{1}I+R_{2}I \end{gathered}$$

Picture drawn by Kirk Betz based on drawing by Dr. Frohnes, lecture Jan. 6, 2010

Magnetic Equations

$\int \overrightarrow{H}d\overrightarrow{l}={ℱ}$

$\oint \overrightarrow{H}d\overrightarrow{l}=Ni=\sum _{n}Hl+Ni=0$

$\oint \overrightarrow{B}d\overrightarrow{s}=0$

$$\begin{gathered} \int \overrightarrow{B}d\overrightarrow{s}=\varphi \approx B{A}_{rea} \\ Magnetic \\ Flux \end{gathered}$$

$$\begin{gathered} R\equiv Reluctance \\ \frac{{ℱ}}{\varphi }=\frac{Ni}{\varphi } \end{gathered}$$

$$\begin{gathered} \overrightarrow{B}=\mu \overrightarrow{H} \\ Assumes \\ Linearity \end{gathered}$$

${ℛ}\frac{l}{\mu A}$