diff --git a/content/book/morrison16_groun_shiel.md b/content/book/morrison16_groun_shiel.md index 6152ff2..ac5cf2c 100644 --- a/content/book/morrison16_groun_shiel.md +++ b/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} - - -{{< 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\\). - + -{{< 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} + + + +{{< 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. + + + +{{< 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} -Morrison, Ralph. 2016. _Grounding and Shielding: Circuits and Interference_. John Wiley & Sons. +Morrison, Ralph. 2016. _Grounding and Shielding: Circuits and Interference_. 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