Update Content - 2021-02-07

content/book/morrison16_groun_shiel.md

@@ -9,7 +9,7 @@ Tags
 
 
 Reference
-: ([Morrison 2016](#org32cff19))
+: ([Morrison 2016](#orgce03fd3))
 
 Author(s)
 : Morrison, R.
@@ -43,10 +43,6 @@ This displacement current flows when charges are added or removed from the plate
 
 ### Introduction {#introduction}
 
-<a id="org3d4e25f"></a>
-
-{{< figure src="/ox-hugo/morrison16_field_conf.png" caption="Figure 1: Field configurations around a shieded conductor" >}}
-
 
 ### Charges and Electrons {#charges-and-electrons}
 
@@ -133,20 +129,72 @@ 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\\).
 
-<a id="org2e6452b"></a>
+<a id="orgb846bd1"></a>
 
-{{< figure src="/ox-hugo/morrison16_H_field.svg" caption="Figure 2: The \\(H\\) field around a current-carrying conductor" >}}
+{{< figure src="/ox-hugo/morrison16_H_field.svg" caption="Figure 1: 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.
+The direction of the force, the direction of the current flow and the direction of the field lines are all perpendicular to each other.
 
 
 ### Ampere's law {#ampere-s-law}
 
+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
+\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.
+Solving for \\(H\\), we obtain
+
+\begin{equation}
+H = \frac{I}{2 \pi r}
+\end{equation}
+
+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 field intensity inside the solenoid is nearly constant, while outside its intensity falls of rapidly.
+
+Using Ampere's law \eqref{eq:ampere_law}:
+
+\begin{equation}
+\oint H dl \approx n I l
+\end{equation}
+
+<a id="orgf50ca35"></a>
+
+{{< figure src="/ox-hugo/morrison16_solenoid.svg" caption="Figure 2: 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).
+The voltage depends on the number of turns in the coil and the rate at which the flux is changing.
+
+<a id="org686ffe9"></a>
+
+{{< figure src="/ox-hugo/morrison16_voltage_moving_coil.svg" caption="Figure 3: A voltage induced into a moving coil" >}}
+
+The magnetic field has two measured.
+The \\(H\\) or magnetic field that is proportional to current flow.
+The force field representation that induces voltage is called the \\(B\\) or induction field.
+The relation between \\(B\\) and \\(H\\) fields is given by:
+
+\begin{equation} \label{eq:relation\_B\_H}
+\boxed{B = \mu\_R \mu\_0 H}
+\end{equation}
+
+where the factor \\(\mu\_0\\) is the permeability of free space and \\(\mu\_R\\) is the relative permeability of the medium.
+
 
 ### The definition of inductance {#the-definition-of-inductance}
 
@@ -624,4 +672,4 @@ Methods for limiting field penetration into and out of a screen are offered.
 
 ## Bibliography {#bibliography}
 
-<a id="org32cff19"></a>Morrison, Ralph. 2016. _Grounding and Shielding: Circuits and Interference_. John Wiley & Sons.
+<a id="orgce03fd3"></a>Morrison, Ralph. 2016. _Grounding and Shielding: Circuits and Interference_. John Wiley & Sons.