Electrostatic & Magnetostatic Field Analysis - Revision history

Kazem Sabet at 21:20, 23 July 2018

2018-07-23T21:20:15Z

2018-06-06T21:52:02Z

‎2D Quasi-Static Solution of TEM Transmission Line Structures

2018-06-06T21:51:46Z

‎2D Quasi-Static Solution of TEM Transmission Line Structures

2017-05-18T15:14:22Z

‎Static Fields Arising from Steady-State Conduction Currents

2017-05-18T15:10:25Z

‎Static Fields Arising from Steady-State Conduction Currents

2017-05-18T15:09:44Z

‎Static Fields Arising from Steady-State Conduction Currents

2017-05-18T15:08:54Z

‎Static Field Arising from Steady-State Conduction Currents

2017-05-18T15:08:35Z

2017-05-18T15:06:01Z

2017-05-18T14:59:17Z

@@ Line 5: / Line 5: @@
 <tr>
 </table>
 == Static Modeling Methods ==

@@ Line 209: / Line 209: @@
 and its characteristic impedance is given by:
-<math> Z_0 = frac{\eta_0}{\sqrt{ \epsilon_{eff}}} = \eta_0 \sqrt{ \frac{C_a}{C} } </math>
+<math> Z_0 = \frac{\eta_0}{\sqrt{ \epsilon_{eff}}} = \eta_0 \sqrt{ \frac{C_a}{C} } </math>
 where &eta;<sub>0</sub> = 120&pi; &Omega; is the intrinsic impedance of the free space.

@@ Line 209: / Line 209: @@
 and its characteristic impedance is given by:
-<math> Z_0 = \eta_0 \sqrt{ \frac{C_a}{C} } </math>
+<math> Z_0 = frac{\eta_0}{\sqrt{ \epsilon_{eff}}} = \eta_0 \sqrt{ \frac{C_a}{C} } </math>
 where &eta;<sub>0</sub> = 120&pi; &Omega; is the intrinsic impedance of the free space.

@@ Line 74: / Line 74: @@
 <math> \mathbf{J(r)} = \sigma \mathbf{E(r)} = -\sigma \nabla \Phi(\mathbf{r}) </math>
-where &sigma; is the electric conductivity. In addition, the continuity equation for a stationary current in a closed region requires that
+where &sigma; is the electric conductivity. On the other hand, the continuity equation for a stationary current requires no charge buildup or decay inside a closed region. This means that
 <math> \nabla . \mathbf{J(r)} = 0 </math>
-These equations lead to the Laplace equation inside an Ohmic conductor medium:
+These above two equations lead to the Laplace equation inside an Ohmic conductor medium:
 <math>\nabla^2 \Phi(\mathbf{r}) = 0</math>

@@ Line 76: / Line 76: @@
 where &sigma; is the electric conductivity. In addition, the continuity equation for a stationary current in a closed region requires that
-<math> \nabla \mathbf{J(r)} = 0 </math>
+<math> \nabla . \mathbf{J(r)} = 0 </math>
 These equations lead to the Laplace equation inside an Ohmic conductor medium:

@@ Line 92: / Line 92: @@
 which can be written as:
-<math> \sigma_1 \hat{\mathbf{n}} . \mathbf{J_1(r)} = \sigma_2 \hat{\mathbf{n}} . \mathbf{J_2(r)}  </math>
+<math> \sigma_1 \hat{\mathbf{n}} . \mathbf{E_1(r)} = \sigma_2 \hat{\mathbf{n}} . \mathbf{E_2(r)}  </math>
 == Magnetostatics Analysis==

@@ Line 68: / Line 68: @@
 <math> \mathbf{E(r)} = - \nabla \Phi(\mathbf{r}) = \frac{1}{4\pi\epsilon}  \int\int\int_V  \frac{\mathbf{r - r^{\prime}} }{ | \mathbf{r - r^{\prime}} |^3 } \rho(\mathbf{r^{\prime}}) dv^{\prime} </math>
-== Static Field Arising from Steady-State Conduction Currents ==
+== Static Fields Arising from Steady-State Conduction Currents ==
 In an Ohmic conductor, the current density is related to the electric field as follows:

@@ Line 84: / Line 84: @@
 In addition, the boundary condition at a conductor-dielectric interface requires a vanishing normal derivative of the electric potential:
-<math> \frac{\partial \Phi}{\partial n} = 0 = 0</math>
+<math> \frac{\partial \Phi}{\partial n} = 0 </math>
 At the interface between two contiguous conductors, the normal component of the current density must be continuous.
 == Magnetostatics Analysis==

← Older revision		Revision as of 14:59, 18 May 2017
Line 67:		Line 67:

	<math> \mathbf{E(r)} = - \nabla \Phi(\mathbf{r}) = \frac{1}{4\pi\epsilon} \int\int\int_V \frac{\mathbf{r - r^{\prime}} }{ \| \mathbf{r - r^{\prime}} \|^3 } \rho(\mathbf{r^{\prime}}) dv^{\prime} </math>		<math> \mathbf{E(r)} = - \nabla \Phi(\mathbf{r}) = \frac{1}{4\pi\epsilon} \int\int\int_V \frac{\mathbf{r - r^{\prime}} }{ \| \mathbf{r - r^{\prime}} \|^3 } \rho(\mathbf{r^{\prime}}) dv^{\prime} </math>
		+
		+	== Static Field Arising from Steady-State Conduction Currents ==
		+
		+	In an Ohmic conductor, the current density is related to the electric field as follows:
		+
		+	<math> \mathbf{J(r)} = \sigma \mathbf{E(r)}</math>
		+
		+	where σ is the electric conductivity. In addition, the continuity equation for a stationary current in a closed region requires that
		+
		+	<math> \nabla \mathbf{J(r)} = 0 </math>
		+
		+	These equations lead to the Laplace equation inside an Ohmic conductor medium:
		+
		+

	== Magnetostatics Analysis==		== Magnetostatics Analysis==