Editing Thunderstorm Generator (section)

= Math & Science =

== Formulas and Equations ==
{| class="wikitable"
|+ Equations Relevant to Thunderstorm Generator Operation
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! Equation !! Description
|-
| <math>E = mc^2</math> || Einstein's equation relating energy (E) to mass (m) and the speed of light (c). Relevant for understanding the potential energy release during atomic processes within the Thunderstorm Generator.
|-
| <math>P = IV</math> || The equation for electrical power (P) as the product of current (I) and voltage (V). Used to calculate the power input/output in electrical components such as the Plasma Injector and [[Plasmoid Generator]].
|-
| <math>F = ma</math> || Newton's second law of motion, defining force (F) as the product of mass (m) and acceleration (a). Relevant for understanding the forces involved in the movement of gases and particles within the Thunderstorm Generator.
|-
| <math>E_{\text{cell}} = E^{\circ}_{\text{cell}} - \frac{RT}{nF}\ln Q</math> || The Nernst equation for calculating the electromotive force (cell potential) of an electrochemical cell at any concentration of reactants and products. Relevant for understanding the electrochemical reactions involved in the electrolysis process within the Thunderstorm Generator.
|-
| <math>KE = \frac{1}{2}mv^2</math> || The equation for kinetic energy (KE) as the product of half the mass (m) and the square of the velocity (v). Relevant for understanding the energy of particles and gases within the Thunderstorm Generator, particularly during combustion and plasma generation processes.
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| <math>\Delta G = \Delta H - T\Delta S</math> || The Gibbs free energy equation, where ΔG represents the change in Gibbs free energy, ΔH represents the change in enthalpy, T represents temperature, and ΔS represents the change in entropy. Relevant for understanding the thermodynamics of chemical reactions, such as the disassociation of water molecules and the formation of plasmoids within the Thunderstorm Generator.
|-
| <math>F = k\frac{q_1q_2}{r^2}</math> || Coulomb's law equation, where F is the electrostatic force between two charged particles, k is Coulomb's constant, q1 and q2 are the magnitudes of the charges, and r is the distance between the charges. Relevant for understanding the interaction between charged particles, such as ions and plasmoids, within the Thunderstorm Generator.
|}
{| class="wikitable"
|+ Constant Values for Plasmoid Equations
! Symbol !! Description !! Value !! Unit !! Scientific Explanation !! Explanation for a 12-Year-Old
|-
| <math>\varepsilon_0</math> || Permittivity of Free Space || <math>8.854 \times 10^{-12}</math> || F/m || Describes how electric fields spread out in empty space. || Imagine space as a giant swimming pool. This number tells us how gooey or watery space is for electric forces. A lower number means it's like swimming through thick, sticky space goo, while a higher number means it's like gliding through smooth, watery space.
|-
| <math>\mu_0</math> || Permeability of Free Space || <math>4\pi \times 10^{-7}</math> || T·m/A || Describes how magnetic fields behave in empty space. || Picture space as a vast landscape. This number tells us how easily magnetic forces can move through space. A smaller number means it's like biking through thick, muddy space, while a larger number means it's like cruising through clear, open space.
|-
| <math>m_e</math> || Electron Mass || <math>9.109 \times 10^{-31}</math> || kg || Mass of an electron, a tiny particle that orbits the nucleus of an atom. || It's like weighing a single grain of sand. It tells us how heavy electrons are, the tiny building blocks of everything around us.
|-
| <math>e</math> || Elementary Charge || <math>1.602 \times 10^{-19}</math> || C || Amount of electric charge carried by a single electron. || Imagine the smallest possible spark of electricity. That's what this number represents – the tiniest bit of electric charge we can imagine. It's like measuring a single drop of water in a vast ocean.
|-
| <math>k_B</math> || Boltzmann Constant || <math>1.381 \times 10^{-23}</math> || J/K || Relates the energy of particles to their temperature in a gas or plasma. || It's like the rulebook for temperature. It helps scientists understand how hot or cold things are in the tiniest detail.
|-
| <math>c</math> || Speed of Light in Vacuum || <math>299,792,458</math> || m/s || How fast light travels in empty space. || It's like the speed record for light. This is how fast light travels through space, which is incredibly fast!
|-
| <math>h</math> || Planck Constant || <math>6.626 \times 10^{-34}</math> || J·s || Relates the energy of a photon to its frequency, helping to understand light and energy. || This number helps us understand how light and energy are related. It's like a special key that unlocks the secrets of light and energy in the universe.
|}
{| class="wikitable"
|+ Plasmoid Equations relevant to Thunderstorm Generator operation
|-
! Equation !! Description !! Use !! Practical Applications
|-
| <math>\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}</math> || Gauss's law for electric fields || Ensures charge conservation and analyzes electric field distributions within plasmoid formations. || Studying plasma confinement and stability in fusion reactors.
|-
| <math>\nabla \cdot \mathbf{B} = 0</math> || Gauss's law for magnetic fields || Analyzes magnetic field distributions within plasmoid formations. || Designing magnetic confinement systems for plasma-based energy generation.
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| <math>\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}</math> || Faraday's law of electromagnetic induction || Understands electromagnetic induction phenomena within plasmoid formations. || Developing advanced induction heating techniques for material processing.
|-
| <math>\nabla \times \mathbf{B} = \mu_0\mathbf{J} + \mu_0\varepsilon_0\frac{\partial \mathbf{E}}{\partial t}</math> || Ampère's law with Maxwell's addition || Analyzes the relationship between electric currents and magnetic fields within plasmoid formations. || Modeling and optimizing magnetic fields in tokamaks for controlled nuclear fusion.
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| <math>\mathbf{E} + \mathbf{v} \times \mathbf{B} = \eta \mathbf{J}</math> || Generalized Ohm's Law || Describes the relationship between electric fields, magnetic fields, and currents in plasmoid formations. || Understanding the behavior of space plasmas and their interactions with magnetic fields.
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| <math>\frac{\partial \mathbf{J}}{\partial t} = \nabla \times \mathbf{B}</math> || Ampère's law with Maxwell's correction || Relates the time rate of change of electric current density to the curl of the magnetic field within plasmoids. || Simulating and predicting magnetic reconnection events in solar flares.
|-
| <math>\nabla \cdot \mathbf{J} = -\frac{\partial \rho}{\partial t}</math> || Continuity equation for electric charge || Ensures conservation of electric charge within plasmoid formations. || Analyzing plasma instabilities and disruptions in fusion experiments.
|}