The Class Notes: Difference between revisions

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Revision as of 16:35, 25 January 2010

4 jan 2010

$L i m i t A \to \infty :$

$X_{0} = \frac{1}{β} X_{s} \Rightarrow V_{0} = \frac{R_{1} + R_{2}}{R_{1}} V_{i n}$

$X_{i} = 0$

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

$V_{i n} = V_{0} (\frac{R_{1}}{R_{1} + R_{2}})$ .

$V_{0} = \frac{1}{(\frac{R_{1}}{R_{1} + R_{2}})} V_{i n}$

Magnetic Circuits

jan 6 2010

$\vec{F} = q \vec{v} \times \vec{B}$

$d \vec{F} = I d \vec{ℓ} \times \vec{B}$

$ℱ = H ℓ_{1} + H ℓ_{2}$

$V = R_{1} I + R_{2} I$

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

Magnetic Equations

$\int \vec{H} d \vec{ℓ} = ℱ$

$\oint \vec{H} d \vec{ℓ} = N i = \sum_{n} H ℓ + N i = 0$

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

$\int \vec{B} d \vec{s} = ϕ \approx B A_{r e a} M a g n e t i c F l u x$

$ℛ \equiv R e l u c t a n c e \frac{ℱ}{ϕ} = \frac{N i}{ϕ}$

$\vec{B} = μ \vec{H} A s s u m e s L i n e a r i t y$

$ℛ \frac{ℓ}{μ A}$

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

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

Magnetic Circuits Examples

What about chancing currents, etc.?

Picture drawn by Kirk Betz based on drawing by Dr. Frohnes, lecture Jan. 8, 2010

$\oint \vec{H} d \vec{ℓ} = N i$

Case i)

$μ = 1 0^{4} μ_{0} i n t h e c o r e$ Something about this part doesn't seem right.

$F i n d \vec{B} i n t h e g a p .$

Graph and picture 6

$H ℓ = N I$ , $I \propto H$

$N I = ℱ ∽ V$

$ℛ = \frac{ℓ}{μ A} ∽ R = \frac{l}{σ A}$

$ϕ = B A ∽ I = J A$

$R_{c} = \frac{ℓ_{1}}{μ A}$

$R_{g} = \frac{g}{μ_{0} (\sqrt{A} + g)^{2}}$

@@ Line 22: / Line 22: @@
 <math> \vec F\ = q \vec v \times \vec B </math>
-<math>d \vec F\ = I d \vec l  \times \vec B </math>
+<math>d \vec F\ = I d \vec\ell \times \vec B </math>
-<math>\mathcal{F} = Hl_1 + Hl_2</math>
+<math>\mathcal{F} = H\ell_1 + H\ell_2</math>
 <math>V\ = R_1I + R_2I</math>
@@ Line 34: / Line 34: @@
 ==Magnetic Equations==
-<math>\int \vec Hd \vec l = \mathcal{F}</math>
+<math>\int \vec Hd \vec\ell= \mathcal{F}</math>
-<math>\oint \vec Hd \vec l = Ni = \sum_{n}Hl + Ni = 0 </math>
+<math>\oint \vec Hd \vec\ell= Ni = \sum_{n}H\ell+ Ni = 0 </math>
 <math>\oint \vec Bd \vec s =  0 </math>
@@ Line 46: / Line 46: @@
 <math> \vec B = \mu \vec H\ Assumes\ Linearity </math>
-<math> \mathcal{R} \frac{l}{\mu A}</math>
+<math> \mathcal{R} \frac{\ell}{\mu A}</math>
 [[Image:BHField.JPG‎]]
@@ Line 64: / Line 64: @@
 Picture drawn by Kirk Betz based on drawing by Dr. Frohnes, lecture Jan. 8, 2010
-<math> \oint \vec Hd \vec l = Ni </math>
+<math> \oint \vec Hd \vec\ell= Ni </math>
 Case i)
@@ Line 74: / Line 74: @@
 Graph and picture 6
-<math> Hl\ = NI </math>, <math>\ I\ \varpropto H</math>
+<math> H\ell\ = NI </math>, <math>\ I\ \varpropto H</math>
 <math> NI\ = \mathcal{F} \backsim V</math>
-<math> \mathcal{R} = \frac{l}{\mu A} \backsim R = \frac{l}{\sigma A} </math>
+<math> \mathcal{R} = \frac{\ell}{\mu A} \backsim R = \frac{l}{\sigma A} </math>
 <math> \phi\ = BA \backsim I = JA</math>
-<math> R_c= \frac{l_1}{\mu A} </math>
+<math> R_c= \frac{\ell_1}{\mu A} </math>
 <math>  R_g= \frac{g}{\mu_0 (\sqrt{A} + g)^2}</math>

The Class Notes: Difference between revisions

Revision as of 16:35, 25 January 2010

Magnetic Circuits

Magnetic Equations

Magnetic Circuits Examples

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