Update Content - 2021-02-07

content/book/morrison16_groun_shiel.md

@@ -5,11 +5,10 @@ draft = false
 +++
 
 Tags
-:
-
+: [Electronics]({{< relref "electronics" >}})
 
 Reference
-: ([Morrison 2016](#orgce03fd3))
+: ([Morrison 2016](#orgdb34704))
 
 Author(s)
 : Morrison, R.
@@ -52,6 +51,10 @@ This displacement current flows when charges are added or removed from the plate
 
 ### Field representation {#field-representation}
 
+<a id="orgb7f2b7d"></a>
+
+{{< figure src="/ox-hugo/morrison16_E_field_charge.svg" caption="Figure 1: The force field lines around a positively chaged conducting sphere" >}}
+
 
 ### The definition of voltage {#the-definition-of-voltage}
 
@@ -61,9 +64,21 @@ This displacement current flows when charges are added or removed from the plate
 
 ### The force field or \\(E\\) field between two conducting plates {#the-force-field-or--e--field-between-two-conducting-plates}
 
+<a id="org9a5dc2a"></a>
+
+{{< figure src="/ox-hugo/morrison16_force_field_plates.svg" caption="Figure 2: The force field between two conducting plates with equal and opposite charges and spacing distance \\(h\\)" >}}
+
 
 ### Electric field patterns {#electric-field-patterns}
 
+<a id="org79f77b7"></a>
+
+{{< figure src="/ox-hugo/morrison16_electric_field_ground_plane.svg" caption="Figure 3: The electric field pattern of one circuit trace and two circuit traces over a ground plane" >}}
+
+<a id="org5199523"></a>
+
+{{< figure src="/ox-hugo/morrison16_electric_field_shielded_conductor.svg" caption="Figure 4: Field configuration around a shielded conductor" >}}
+
 
 ### The energy stored in an electric field {#the-energy-stored-in-an-electric-field}
 
@@ -73,6 +88,10 @@ This displacement current flows when charges are added or removed from the plate
 
 ### The \\(D\\) field {#the--d--field}
 
+<a id="org6d533a1"></a>
+
+{{< figure src="/ox-hugo/morrison16_E_D_fields.svg" caption="Figure 5: The electric field pattern in the presence of a dielectric" >}}
+
 
 ### Capacitance {#capacitance}
 
@@ -129,11 +148,11 @@ In a few elements, the atomic structure is such that atoms align to generate a n
 The flow of electrons is another way to generate a magnetic field.
 
 The letter \\(H\\) is reserved for the magnetic field generated by a current.
-Figure [1](#orgb846bd1) shows the shape of the \\(H\\) field around a long, straight conductor carrying a direct current \\(I\\).
+Figure [6](#org4c94f50) shows the shape of the \\(H\\) field around a long, straight conductor carrying a direct current \\(I\\).
 
-<a id="orgb846bd1"></a>
+<a id="org4c94f50"></a>
 
-{{< figure src="/ox-hugo/morrison16_H_field.svg" caption="Figure 1: The \\(H\\) field around a current-carrying conductor" >}}
+{{< figure src="/ox-hugo/morrison16_H_field.svg" caption="Figure 6: The \\(H\\) field around a current-carrying conductor" >}}
 
 The magnetic field is a force field.
 This force can only be exerted on another magnetic field.
@@ -145,10 +164,10 @@ The direction of the force, the direction of the current flow and the direction
 Ampere's law states that the integral of the \\(H\\) field intensity in a closed-loop path is equal to the current threading that loop
 
 \begin{equation} \label{eq:ampere\_law}
-\oint H dl = I
+\boxed{\oint H dl = I}
 \end{equation}
 
-The simplest path to use for this integration is the one of the concentric circles in Figure [1](#orgb846bd1), where \\(H\\) is constant and \\(r\\) is the distance from the conductor.
+The simplest path to use for this integration is the one of the concentric circles in Figure [6](#org4c94f50), where \\(H\\) is constant and \\(r\\) is the distance from the conductor.
 Solving for \\(H\\), we obtain
 
 \begin{equation}
@@ -160,7 +179,7 @@ And we see that \\(H\\) has units of amperes per meter.
 
 ### The solenoid {#the-solenoid}
 
-The magnetic field of a solenoid is shown in Figure [2](#orgf50ca35).
+The magnetic field of a solenoid is shown in Figure [7](#org7682896).
 The field intensity inside the solenoid is nearly constant, while outside its intensity falls of rapidly.
 
 Using Ampere's law \eqref{eq:ampere_law}:
@@ -169,20 +188,20 @@ Using Ampere's law \eqref{eq:ampere_law}:
 \oint H dl \approx n I l
 \end{equation}
 
-<a id="orgf50ca35"></a>
+<a id="org7682896"></a>
 
-{{< figure src="/ox-hugo/morrison16_solenoid.svg" caption="Figure 2: The \\(H\\) field around a solenoid" >}}
+{{< figure src="/ox-hugo/morrison16_solenoid.svg" caption="Figure 7: The \\(H\\) field around a solenoid" >}}
 
 
 ### Faraday's law and the induction field {#faraday-s-law-and-the-induction-field}
 
 When a conducting coil is moved through a magnetic field, a voltage appears at the open ends of the coil.
-This is illustrated in Figure [3](#org686ffe9).
+This is illustrated in Figure [8](#org431ab1d).
 The voltage depends on the number of turns in the coil and the rate at which the flux is changing.
 
-<a id="org686ffe9"></a>
+<a id="org431ab1d"></a>
 
-{{< figure src="/ox-hugo/morrison16_voltage_moving_coil.svg" caption="Figure 3: A voltage induced into a moving coil" >}}
+{{< figure src="/ox-hugo/morrison16_voltage_moving_coil.svg" caption="Figure 8: A voltage induced into a moving coil" >}}
 
 The magnetic field has two measured.
 The \\(H\\) or magnetic field that is proportional to current flow.
@@ -195,18 +214,95 @@ The relation between \\(B\\) and \\(H\\) fields is given by:
 
 where the factor \\(\mu\_0\\) is the permeability of free space and \\(\mu\_R\\) is the relative permeability of the medium.
 
+For an area of constant field intensity, the magnetic flux \\(\phi\\) is simply the product \\(BA\\) where \\(B\\) is in tesla, \\(A\\) is the area in square meters, and \\(\phi\\) is the flux in webers.
+
+The voltage induced in a conducting coil is given by the **Faraday's law**:
+
+\begin{equation} \label{eq:faraday\_law}
+\boxed{V = n \frac{d\phi}{dt} = n A \frac{dB}{dt}}
+\end{equation}
+
+where \\(n\\) is the number of turns in the coil.
+If the induction flux \\(B\\) increases linearly, a steady voltage \\(B\\) must exist at the coil ends.
+The inverse is also true.
+
 
 ### The definition of inductance {#the-definition-of-inductance}
 
+<div class="definition">
+  <div></div>
+
+Inductance is defined as the ratio of magnetic flux generated per unit current.
+The unit of inductance if the henry.
+
+</div>
+
+For the  coil in Figure [7](#org7682896):
+
+\begin{equation} \label{eq:inductance\_coil}
+V = n^2 A k \mu\_0 \frac{dI}{dt} = L \frac{dI}{dt}
+\end{equation}
+
+where \\(k\\) relates to the geometry of the coil.
+
+Equation \eqref{eq:inductance_coil} states that if \\(V\\) is one volt, then for an inductance of one henry, the current will rise at the rate of one ampere per second.
+
 
 ### The energy stored in an inductance {#the-energy-stored-in-an-inductance}
 
+One way to calculate the work stored in a magnetic field is to use Eq. \eqref{eq:inductance_coil}.
+The voltage \\(V\\) applied to a coil results in a linearly increasing current.
+At any time \\(t\\), the power \\(P\\) supplied is equal to \\(VI\\).
+Power is the rate of change of energy or \\(P = d\bm{E}/dt\\) where \\(\bm{E}\\) is the stored energy in the inductance.
+We then have the stored energy in an inductance:
+
+\begin{equation} \label{eq:energy\_inductance}
+\boxed{\bm{E} = L \int\_0^I I dI = \frac{1}{2} L I^2}
+\end{equation}
+
+<div class="important">
+  <div></div>
+
+An inductor stores field energy.
+It does not dissipate energy.
+
+</div>
+
+The presence of a voltage \\(V\\) on the terminals of an inductor implies an electric field.
+The movement of energy into the inductor thus requires both an electric and a magnetic field.
+This is due to the Faraday's law that requires a voltage when changing magnetic flux couples to a coil.
+
+<div class="exampl">
+  <div></div>
+
+Consider a 1mH inductor carrying a current of 0.1A.
+The stored energy is \\(5 \times 10^{-4} J\\).
+Assume the shunt capacitance equals 100pF.
+When this energy is fully transferred to the capacitance, the voltage must be 3116 V.
+This would probably destroy the component.
+
+In order to absorb the stored magnetic field energy and avoid a high voltage, a reverse diode accross the coil can be used to provide a path for interrupted current flow.
+
+</div>
+
 
 ### Magnetic field energy in space {#magnetic-field-energy-in-space}
 
+The energy \\(\bm{E}\\) stored is
+
+\begin{equation}
+\bm{E} = \frac{1}{2} \frac{B^2 \bm{V}}{\mu\_0}
+\end{equation}
+
+where is volume \\(\bm{V} = Ad\\) and \\(\mu\_0\\) is the permeability of free space.
+
 
 ### Electron drift {#electron-drift}
 
+Current flow in conductors is the movement of charge.
+The velocity of energy flow is the speed of light, but the average velocity of electrons in a typical circuit is extremely low.
+In a typical circuit, conductor carrying current, the average electron velocity is less than 0.025mm/s.
+
 
 ## Digital Electronics {#digital-electronics}
 
@@ -672,4 +768,4 @@ Methods for limiting field penetration into and out of a screen are offered.
 
 ## Bibliography {#bibliography}
 
-<a id="orgce03fd3"></a>Morrison, Ralph. 2016. _Grounding and Shielding: Circuits and Interference_. John Wiley & Sons.
+<a id="orgdb34704"></a>Morrison, Ralph. 2016. _Grounding and Shielding: Circuits and Interference_. John Wiley & Sons.