Differences

This shows you the differences between two versions of the page.

--- maxwell_original_equations [2023/08/13 06:02] – [Magnetic Displacement Field Vector] joellagace
+++ maxwell_original_equations [2023/08/15 17:34] (current) – [Magnetic Field Vector] joellagace
@@ Line 101: / Line 101: @@
 You can picture this scenario like the Earth's magnetic field. Visualize the Earth with field lines emerging from the North magnetic pole and entering the South magnetic pole, similar to how we illustrate the Earth's magnetic field in geography textbooks.
+***Note**
+In the study of magnetism, one of the most familiar visuals is the magnetic field of a bar magnet. Lines of force seem to emerge from the north pole, loop around, and return to the south pole, creating a clear magnetic "circuit". While this understanding serves as the foundation for conventional wisdom on the subject, a surge of interest from emerging scientists and innovators suggests that there are nuances to this paradigm which have yet to be fully explored. Two noteworthy contributions come from Howard Johnson and Edward Leedskalnin.
+**Howard Johnson and the Magnetic Gate:**
+Howard Johnson, a notable figure in the domain of magnetism, dedicated much of his life to investigating the intricacies of magnetic fields. His most striking discovery was the "magnetic gate", an arrangement of magnets that, as per Johnson's claims, would allow for a continuous motion, leading some to speculate about the possibility of perpetual motion machines.
+Central to Johnson's work is the idea that magnets do not have a single, uniform magnetic field. Instead, they possess multiple, distinct fields, each interacting differently based on its alignment and proximity to other magnets. This discovery challenges the conventional understanding of magnetic interaction, proposing that with the right arrangement, one could harness these unique magnetic fields for practical applications, such as the aforementioned magnetic gate.
+**Edward Leedskalnin's Vortex Theory:**
+Edward Leedskalnin, though a less conventional scientist, brought another layer of insight to this magnetic debate. Leedskalnin, the creator of the Coral Castle in Florida, postulated his own theories on magnetism, emphasizing the role of individual "magnet particles" or "little magnets".
+In Leedskalnin's perspective, when arranging these "little magnets" from north to south, they exhibit a distinct pattern: one line of magnets will align North-South-North-South and so forth, while the subsequent line will align in the opposite manner, South-North-South-North. This alternating pattern, according to Leedskalnin, results in the creation of dual vortices, providing a fresh perspective on how magnetic fields may operate.
+The study of magnetism, like many areas of science, is an evolving field. While traditional models provide foundational knowledge, contributions from thinkers like Johnson and Leedskalnin emphasize that there is always room for re-evaluation and discovery. As we move forward, it's essential to keep an open mind, embracing both conventional wisdom and the insights of those who view the magnetic world through a different lens.
 **Conclusion:**
@@ Line 626: / Line 644: @@
 Imagine you're in a forest with trees of varying densities. The magnetic field **B** is like the actual number of trees you see in any patch of land. Now, suppose there are certain invisible magical trees that only special beings (hypothetical magnetic monopoles) can interact with. The total trees, including these magical ones, represent the magnetic displacement field **Dm**. It encapsulates both the regular trees and the presence of these special trees.
+==== Magnetic Field Intensity for Magnetic Charges Vector ====
 H_m: Magnetic field intensity for magnetic charges vector, with three components (H_mx, H_my, H_mz).
+The **Hm** vector, or the magnetic field intensity for magnetic charges, is a theoretical construct, mirroring the **H** (magnetic field intensity) in the realm of the hypothetical magnetic charges. In essence, while **H** provides a measure of the magnetic field produced by electric currents, **Hm** would describe the field produced by the movement of magnetic charges.
+**Example:**
+Suppose we have a magnetic field given by: {{:b_234.png?nolink&200|}}
+And a hypothetical magnetic current density vector: {{:jm.png?nolink&200|}}
+Using the relationship: {{:hm.png?nolink&200|}}
+And taking {{:uo.png?nolink&200|}}
+{{:hm_.png?nolink&400|}}
+After calculation, you'll get an **Hm** vector with very large values due to the division by the small value of μo , minus the contributions of the magnetic current density vector.
+**Technical Details:**
+  - **Definition:** Given the existence of magnetic monopoles, **Hm** would be defined analogously to **H** in relation to the magnetic field **B** and the hypothetical magnetic current density **Jm**. This relationship would be expressed as: {{:hmjm.png?nolink&150|}}where μo is the permeability of free space.
+  - **Relation with Magnetic Field:** Just as **H**  relates to the electric currents that generate a magnetic field, **Hm** would be related to hypothetical magnetic currents generating a magnetic field.
+  - **Units:** The units of **Hm** would be A/m (Amperes per meter), representing the hypothetical magnetic current per unit length.
+**Visual Representation**
+Imagine a river with water currents flowing through it, which represents our familiar electric current in the context of magnetic fields. Now, picture another parallel river, but instead of water, it flows with a silvery, magnetic liquid. This is our hypothetical magnetic current. The flow intensity and direction of this magnetic river represent the **Hm** vector.
+==== Free Magnetic Charge Density Scalar ====
 ρ_fm: Free magnetic charge density scalar, or the hypothetical amount of free magnetic charge per unit volume.
+Just as electric charge density **(p)** represents the amount of electric charge in a given volume, **Pfm** would theoretically represent the amount of magnetic charge in a given volume.
+**Example:**
+Imagine a cubic container with a side length of 1 meter, suspended in space. Now, let's assume that within this cube, there's a mist or fog representing our magnetic charge. The density of this mist—how thick or thin it is—symbolizes our **Pfm**.
+To make it tangible:
+  * Let's assume there are 10 hypothetical magnetic monopoles within this 1m^3 box. Each monopole carries a magnetic charge of 0.1 A·m.
+  * To find the free magnetic charge density, **Pfm**,  for this cube: {{:pfm.png?nolink&200|}}
+Substitute in the given values: {{:pfmam.png?nolink&200|}}
+This result means that, on average, there's a magnetic charge equivalent to 1 A·m in every cubic meter of our container.
+**Visual Representation**
+In visual terms, if you were to look at this box from the outside, the density of the mist inside would be uniform, reflecting the even spread of these hypothetical magnetic charges throughout the space. The thicker the mist, the greater the magnetic charge density.
+==== Free Magnetic Current Density Vector ====
 J_fm: Free magnetic current density vector, which has three components (J_fmx, J_fmy, J_fmz) and represents the hypothetical density of free flowing magnetic charge.
+Now, much like we can measure the volume of water flowing through a section of a river per unit time (liter/sec), the "free magnetic current density" measures the amount of these magnetic charges flowing through a certain area in a certain time, but in all three dimensions.
+**Technical Details:**
+  * **J_fm** is a vector, meaning it has a direction and a magnitude. Each of its components (J_fmx, J_fmy, J_fmz) represents the magnetic current in the x, y, and z directions, respectively.
+  * **Units**: Given that current is the rate of flow of charge, and considering that our charges here are magnetic monopoles, the unit would be Am^-2 (Amperes per square meter).
+**Example Visualization:**
+**1. Imagine a 3D grid box in space.**
+  * The length of the box represents the x-direction.
+  * The width represents the y-direction.
+  * The height represents the z-direction.
+**2. Picture magnetic monopoles as tiny blue glowing spheres** flowing through this box, kind of like glowing water droplets moving in different directions.
+**3. Measure the Flow:**
+  * Assume we have 100 monopoles flowing through the x-face (length) of our 1m^2 box face every second. This means, J_fmx = 100 Am^-2.
+  *  For the y-face (width), assume 50 monopoles flow through per second. Thus, J_fmy = 50 Am^-2.
+  * For the z-face (height), let's say there's no flow (or the monopoles are stationary). Then, J_fmz = 0 Am^-2.
+**4. Resulting Vector:**
+Thus, our J_fm or free magnetic current density vector can be represented as:
+J_fm = <100, 50, 0> Am^-2
+This vector points more in the direction of the x-axis than the y-axis, indicating that there's a stronger flow of magnetic monopoles in the x-direction than the y-direction in our hypothetical box.
+**Interpretation:**
+This example helps illustrate how J_fm can be used to represent the direction and magnitude of flow of hypothetical magnetic monopoles in space. By knowing the value of J_fm in a particular region, one can understand the behavior and flow dynamics of these monopoles, much like understanding water current in different parts of a river.
+==== Electrodynamic Potential Scalar ====
 ϕ_e: Electrodynamic potential scalar.
+This potential is rather about electric fields. The electrodynamic potential scalar, determines how much potential energy a unit charge has due to electric fields in a particular point in space.
+**Technical Details:**
+  * **ϕ_e** is a scalar, which means it has a magnitude but no direction. It represents the electric potential energy per unit charge at a given point in space.
+  * **Units**: Given that it's potential energy per unit charge, the unit for electrodynamic potential scalar is volts (V).
+**Example Visualization:**
+**1. The Landscape of Electric Potential:**
+Imagine a landscape with hills, valleys, and flat areas. Each point on this landscape represents a point in space.
+**2. Visualize the Heights:**
+  * High peaks on this landscape symbolize areas with high positive electric potential. Picture them as glowing bright golden regions.
+  * Deep valleys represent areas with high negative electric potential. Visualize these valleys as glowing deep blue.
+  * Flat areas or gentle slopes indicate regions with minimal or no electric potential, visualized as neutral colors.
+**3. Movement on this Landscape:**
+If you were to place a positive test charge on this landscape, it would naturally be attracted to the blue valleys (representing negative potential) and repelled from the golden peaks (positive potential), much like water flows downhill due to gravity.
+**4. Measurement:**
+Imagine standing on a glowing golden peak. The brightness and height of the peak give you the value of **ϕ_e** at that point. If it's very bright and high, **ϕ_e** might be, say, +100V. If you stand in a deep blue valley, the depth and intensity of the blue might represent a potential of -100V. A flat, neutral area might represent a potential of 0V.
+**Interpretation:**
+The electrodynamic potential scalar, **ϕ_e**, provides a way to visualize the "landscape" of electric potential in space. Knowing the value of **ϕ_e** at any point allows us to predict the behavior of charged particles in that region. High positive potentials will repel positive charges, and high negative potentials will attract them. By understanding this "landscape," we can predict and explain the movement of electric charges, similar to predicting the path water might take on a hilly terrain.
+==== Magneto-dynamic Potential Scalar ====
 ϕ_m: Magneto-dynamic potential scalar.
+To understand the concept of the magneto-dynamic potential scalar, let's take the analogy of water currents in an ocean. The deeper you go into the ocean, the stronger and more unpredictable the currents become. These currents represent magnetic fields. The depth at which you are in the ocean can be seen as a measure of the magneto-dynamic potential — deeper depths equate to greater potential.
+**Technical Details:**
+  * **ϕ_m** is a scalar, which means it possesses magnitude but no direction. It represents the magnetic potential energy per unit magnetic charge (hypothetical) at a specific point in space.
+  * **Units**: Given it's potential energy per unit magnetic charge, the unit for magneto-dynamic potential scalar would be analogous to volts but for magnetic fields. For our discussions, let's represent it as "magvolts" (Mv), though this isn't a standard unit.
+**Example Visualization:**
+**1. The Ocean of Magnetic Potential:**
+Imagine a vast, deep ocean. The surface represents regions with minimal magnetic potential, and as we go deeper, the magnetic potential increases.
+**2. Visualize the Depths:**
+  * The dark abyssal zones of the ocean symbolize areas with high negative magnetic potential. Picture these zones as filled with fast, swirling currents, glowing with a deep blue luminescence.
+  * Sunlit shallows represent areas with high positive magnetic potential. These regions shimmer with golden light and have gentle, predictable currents.
+  * The mid-depths, neither too dark nor too bright, indicate regions with moderate magnetic potential.
+**3. Movement in this Ocean:**
+If you were to release a hypothetical magnetic monopole into this ocean, its behavior would be determined by the depths. Positive magnetic monopoles would dive deep into the abyssal zones, attracted by the strong currents of the negative magnetic potential. Negative monopoles, conversely, would float upwards to bask in the golden shallows of positive magnetic potential.
+**4. Measurement:**
+Imagine you're a diver in this ocean. The depth and intensity of the currents around you provide a measure of** ϕ_m** at your location. In a fast, swirling abyssal zone, **ϕ_m** might be -100Mv. In the golden-lit shallows, it could be +50Mv. In the moderate mid-depths, it might be close to 0Mv.
+**Interpretation:**
+The magneto-dynamic potential scalar, **ϕ_m**, allows us to visualize the "ocean" of magnetic potential in a region. By knowing its value at any point, we can predict the behavior of hypothetical magnetic charges in that vicinity. This oceanic analogy helps to illustrate the complex interplay of magnetic fields and the resulting potentials, guiding the movements and interactions of magnetic entities within them.
 ==== The Original Equations ====
@@ Line 644: / Line 811: @@
 Maxwell's equations originally made use of a "sea of molecular vortices" in the luminiferous aether. This was a mechanical view of the aether, but it's the context in which his 20 equations were formulated.
-The original 20 equations can be somewhat intimidating because of their number, but also due to the context in which they were formulated. Here is a broad overview:
+The original 20 equations can be somewhat intimidating because of their number, but also due to the context in which they were formulated. Here is a broad review:
 === Electric field equations: ===
@@ Line 656: / Line 823: @@
   * Divergence of the magnetic field B
   * Curl of the magnetic field H
   * Definition of B in terms of the magnetic field H