Update Content - 2021-02-07
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@ -9,7 +9,7 @@ Tags
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Reference
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: ([Morrison 2016](#org32cff19))
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: ([Morrison 2016](#orgce03fd3))
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Author(s)
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: Morrison, R.
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@ -43,10 +43,6 @@ This displacement current flows when charges are added or removed from the plate
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### Introduction {#introduction}
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<a id="org3d4e25f"></a>
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{{< figure src="/ox-hugo/morrison16_field_conf.png" caption="Figure 1: Field configurations around a shieded conductor" >}}
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### Charges and Electrons {#charges-and-electrons}
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@ -133,20 +129,72 @@ In a few elements, the atomic structure is such that atoms align to generate a n
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The flow of electrons is another way to generate a magnetic field.
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The letter \\(H\\) is reserved for the magnetic field generated by a current.
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Figure [1](#orgb846bd1) shows the shape of the \\(H\\) field around a long, straight conductor carrying a direct current \\(I\\).
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<a id="org2e6452b"></a>
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<a id="orgb846bd1"></a>
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{{< figure src="/ox-hugo/morrison16_H_field.svg" caption="Figure 2: The \\(H\\) field around a current-carrying conductor" >}}
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{{< figure src="/ox-hugo/morrison16_H_field.svg" caption="Figure 1: The \\(H\\) field around a current-carrying conductor" >}}
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The magnetic field is a force field.
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This force can only be exerted on another magnetic field.
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The direction of the force, the direction of the current flow and the direction of the field lines are all perpendicular to each other.
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### Ampere's law {#ampere-s-law}
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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
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\begin{equation} \label{eq:ampere\_law}
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\oint H dl = I
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\end{equation}
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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.
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Solving for \\(H\\), we obtain
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\begin{equation}
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H = \frac{I}{2 \pi r}
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\end{equation}
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And we see that \\(H\\) has units of amperes per meter.
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### The solenoid {#the-solenoid}
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The magnetic field of a solenoid is shown in Figure [2](#orgf50ca35).
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The field intensity inside the solenoid is nearly constant, while outside its intensity falls of rapidly.
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Using Ampere's law \eqref{eq:ampere_law}:
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\begin{equation}
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\oint H dl \approx n I l
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\end{equation}
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<a id="orgf50ca35"></a>
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{{< figure src="/ox-hugo/morrison16_solenoid.svg" caption="Figure 2: The \\(H\\) field around a solenoid" >}}
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### Faraday's law and the induction field {#faraday-s-law-and-the-induction-field}
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When a conducting coil is moved through a magnetic field, a voltage appears at the open ends of the coil.
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This is illustrated in Figure [3](#org686ffe9).
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The voltage depends on the number of turns in the coil and the rate at which the flux is changing.
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<a id="org686ffe9"></a>
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{{< figure src="/ox-hugo/morrison16_voltage_moving_coil.svg" caption="Figure 3: A voltage induced into a moving coil" >}}
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The magnetic field has two measured.
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The \\(H\\) or magnetic field that is proportional to current flow.
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The force field representation that induces voltage is called the \\(B\\) or induction field.
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The relation between \\(B\\) and \\(H\\) fields is given by:
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\begin{equation} \label{eq:relation\_B\_H}
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\boxed{B = \mu\_R \mu\_0 H}
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\end{equation}
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where the factor \\(\mu\_0\\) is the permeability of free space and \\(\mu\_R\\) is the relative permeability of the medium.
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### The definition of inductance {#the-definition-of-inductance}
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@ -624,4 +672,4 @@ Methods for limiting field penetration into and out of a screen are offered.
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## Bibliography {#bibliography}
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<a id="org32cff19"></a>Morrison, Ralph. 2016. _Grounding and Shielding: Circuits and Interference_. John Wiley & Sons.
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<a id="orgce03fd3"></a>Morrison, Ralph. 2016. _Grounding and Shielding: Circuits and Interference_. John Wiley & Sons.
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