class: center, middle # EE-362 ELECTROMECHANICAL ENERGY CONVERSION-II ## Ozan Keysan [ozan.keysan.me](http://ozan.keysan.me) Office: C-113
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Tel: 210 7586 --- ## Who is this guy?
--- ## [James Clerk Maxwell](https://en.wikipedia.org/wiki/James_Clerk_Maxwell)
--- # Maxwell Equations ### $$ \nabla\cdot{\bf E} = \dfrac{\rho}{\epsilon_0} $$ ### $$ \nabla\cdot{\bf B} = 0 $$ ### $$ \nabla\times{\bf E} = - {{\partial{\bf B}}\over{\partial t}} $$ ### $$ \nabla\times{\bf H} = {\bf J} + {\epsilon_0{\partial{\bf E}}\over{\partial t}} $$ #### [More info](http://www.maxwells-equations.com/), [Who's afraid of Maxwell equations?](http://majr.com/docs/Whos_Afraid_of_Maxwells_Equations_By_Elya_Joffe.pdf) --- # Need a reminder for vector calculus? #[Divergence](http://betterexplained.com/articles/divergence/): \\(\nabla\cdot\\) --
--- #[Divergence](http://betterexplained.com/articles/divergence/): \\(\nabla\cdot\\)
--- # Need a reminder for vector calculus? #[Curl](http://betterexplained.com/articles/divergence/): \\(\nabla\times\\) --
--- #[Curl](http://betterexplained.com/articles/divergence/): \\(\nabla\times\\)
--- # Maxwell Equations: ### $$\textrm{Gauss' Law}\quad \nabla \cdot \vec{E} = \frac{\rho}{\varepsilon_0} $$ -- ### $$\textrm{Gauss' Law ($\vec{B}$ Fields)} \quad \nabla \cdot \vec{B} = 0 $$ --- # Maxwell Equations: ### $$\textrm{Faraday's Law} \quad \nabla \times \vec{E} = - \frac{\partial \vec{B}}{\partial t}$$ -- ### $$\textrm{Ampere's Law} \quad \nabla \times \vec{H} = \vec{J} + \varepsilon_0\frac{\partial \vec{E}}{\partial t}$$ ### [More info](http://www.maxwells-equations.com/), [Who's afraid of Maxwell equations?](http://majr.com/docs/Whos_Afraid_of_Maxwells_Equations_By_Elya_Joffe.pdf) --- # Maxwell Equations: ## $$\textrm{Gauss' Law:}\quad \nabla \cdot \vec{E} = \frac{\rho}{\varepsilon_0} $$ ## Integral form: ## $$\oint_S {E dA} = {Q \over \varepsilon_0}$$ --- # Maxwell Equations: ## Gauss' Law(Magnetic Field): ### $$\nabla \cdot \vec{B} = 0 $$ ### $$\oint_S {B dA} = 0$$ -- ### Practical Meaning: ### - There are no magnetic flux sources. ### - No magnets with single pole! --- # Maxwell Equations: Faraday's Law ### $$\nabla \times \vec{E} = - \frac{\partial \vec{B}}{\partial t}$$ -- ### $$\oint_C \vec{E} dl = - \frac{\partial \Phi}{\partial t} = -\frac{d}{dt}\iint B dA$$ ### !! The most important equation for EE362 ### [Induction Melting](https://www.youtube.com/watch?v=8i2OVqWo9s0), [Levitation](https://www.youtube.com/watch?v=txmKr69jGBk) --- # Maxwell Equations: Ampere's Law ### $$ \nabla \times \vec{H} = \vec{J} + \varepsilon_0\frac{\partial \vec{E}}{\partial t}$$ -- ### Neglect the [displacement current](https://en.wikipedia.org/wiki/Amp%C3%A8re%27s_circuital_law) part. ### $$\oint_C {\vec{H}.d\vec{\ell}} = \iint \vec{J}dA = \sum I_n $$ --- # Ohm's Law (for Magnetic Circuit) ### Electric Circuits: ### $$V=IR$$ -- ### Magnetic Circuits ### $$\mathcal{F} = \Phi \mathcal{R}$$ -- ### Reluctance ### $$\mathcal{R} = \frac{l}{\mu A}$$ --- # Current Density vs. Magnetic Flux Density ## Current Density = Conductivity x Electric Field ## $$\vec{J}=\rho \vec{E}$$ -- ## Flux Density = Permeability x Magnetic Field ## $$\vec{B} = \mu \vec{H}$$ --- # Suggested Review from EE361 - # Magnetic Circuits - # Equivalent Circuit of Transformers - # Phasors - # Three phase power --- ## You can download this presentation from: [keysan.me/ee362](http://keysan.me/ee362)