From 5cc34003d97acf2b90d1204ea968a83d66210b95 Mon Sep 17 00:00:00 2001 From: Mars Ultor Date: Mon, 17 Feb 2025 18:19:24 -0600 Subject: [PATCH] hahah --- content/physics/CrazyStuff.md | 108 +++++++++++++++++++++ content/physics/swappy-20250215-165128.png | Bin 0 -> 48506 bytes 2 files changed, 108 insertions(+) create mode 100644 content/physics/CrazyStuff.md create mode 100644 content/physics/swappy-20250215-165128.png diff --git a/content/physics/CrazyStuff.md b/content/physics/CrazyStuff.md new file mode 100644 index 0000000..59523b5 --- /dev/null +++ b/content/physics/CrazyStuff.md @@ -0,0 +1,108 @@ +--- +title: Crazy Mix of Everything You Could Dread +date: 2025-02-15 +--- + +# Electric Charge and Electric Field + +## Laws? + +1. *Law of Conservation of Electric Charge*: **the net amount of electric charge produced in any process is zero**. + +2. I forgot + +## Insulators and Conductors + +This image should sum things up nicely. + +![](swappy-20250215-165128.png) + +## Coulomb's Law + +$$ +||\vec{F}||=k\frac{Q_1 Q_2}{r^2} +$$ + +$k$ is a random constant written in terms of a more definite constant such that: + +$$ +F=\frac{1}{r\pi\epsilon_0}\frac{Q_1 Q_2}{r_2} +$$ +where +$$ +\epsilon_0=\frac{1}{4\pi k}=8.85\times 10^{-12}\;\text{ C}^2/\mathrm{N}*\mathrm{m}^2 +$$ + +It's important to consider here, that $r$ is the magnitude of distance, and $F$ always represents the magnitude of the force. Oppositely signed charges attract, and same-signed charges repel with the force computed by the formula. + +# The Electric Field + +$$ +\vec{E}=\frac{\vec{F}}{q} +$$ + +- $q$ is the magnitude of the charge +- The electric field only reflects the *direction* of the magnetic field, not the intensity. +- The electric field $\vec{E}$ represents the force per unit charge, so really: + +$$ +\vec{E}=\lim_{q\to 0}{\vec{F}/q} +$$ + +The electric field has the units Newtons per Coulomb: N/C. The magnitude of the electric field vector $\vec{E}$, can be calculated as $E$: +$$ +E=\frac{F}{q}=\frac{kqQ/r^2}{q} = k\frac{Q}{r^2} +$$ + + +Notice that the vector field $\vec{E}$ is independent of the test charge $q$, only dependent on the parent charge $Q$ that produces the field. $\therefore$, the force experienced by a particle at a given position $r$ can be expressed by: + +$$ +\vec{F}=q\vec{E} +$$ + +If there are more than one parent charge $Q$, the experienced electric vector field is simply: + +$$ +\vec{E}=\vec{E_1}+\vec{E_2}+\vec{E_n} +$$ + +# Electric Potential Energy and Potential Difference + +A fundamental law of physics is that $\Delta \textbf{PE} =-W$, while the change in kinetic energy is oppositely signed. The potential difference between any two points is $\textbf{PE}_b-\textbf{PE}_a$, while work is expressed like so: + +$$ +W=\int{F\mathrm{d}r} +$$ + +> [!NOTE] +> $r$ and $x$ are used interchangeably for displacement. $r$ is more commonly seen in multi-dimensional reference frames. + +$\therefore$ the work done by electric field $\vec{E}$ is: + +$$ +W=Fd=-qEd +$$ +$$\Delta \textbf{PE}=-qEd +$$ + +This is only true if the electric field is uniform. In reality, it never is. + +## Potential Difference + +**Electric Potential** is understood as the electric potential energy per unit charge. This variable is given the symbol $V$. At some displacement $a$ from the parent charge $Q$: + +$$ +V_a=\frac{\textbf{PE}_a}{q} +$$ + +Two balls at the same height are not meaningfully different in position, therefore only *potential difference* matters physically. In this case, between two points, $a$ and $b$. When the electric force does positive work on a charge, the kinetic energy increases in tandem with a decrease of that potential difference. Keeping in line with the rules laid out above: + +$$ +V_{ba}=V_b-V_a=\frac{\Delta \textbf{PE}_{ba}}{q}=\frac{-W_{ba}}{q} +$$ + +Just as the potential energy of a raised ball does not depend on the gravitational field of the ball, the electric potential of the test charge $q$ doesn't depend on the magnitude of the charge itself. This quantity is given the unit **Volt**, or $1\text{ V}=1\;\text{J}/\mathrm{C}$ + +--- +#physics diff --git a/content/physics/swappy-20250215-165128.png b/content/physics/swappy-20250215-165128.png new file mode 100644 index 0000000000000000000000000000000000000000..19bef5b8d41138b004e57fafc80d34c8d1748f6b GIT binary patch literal 48506 zcmeAS@N?(olHy`uVBq!ia0y~yU^HW3VAAGbVqjo+Ri~uJz`(#m_VpoIIUjq4{i~sJItwLROXf z3tQM*#1t9~1*+6Jbschoc^HH5@=8R%+op4JQ53J*#HzKykfEQtMn|cX(v& z5GsABwDO_XmDcVhZO9T|ygIjS-I{x6L*my}q0!rNIN6$ul$ECC-OrO1=3ue=f4*Mm z$^ktGXXnG_@%3|GgsJGCI&~^+ebm$!VP9CbxR@vCAFzzyk#JCY{oa3vzu!0R?Uk|I zv~1b7txHo+U0G?|Z?$So4!h!$gYEMFaxN~<-~ad8_V{{X4wh|G^6vkwoXpvlxaY&2 z&;NhE+5A3yy_|L4o2GudTk|(xy>`v+(}(!!x{*rOo9@Tde4H8{FIswL)l}{O|Bl@U z38!z6F{!-7DjxUabNrvA`hDAf2LuIudS?Ic=hyJ~sc&x-{*p|WG0Kfv6n#bcz`ce~ zpFZ7OK0h!f;>+p9{r|qr&Oh{U!=1R;*xKJ~xA$pD1;#{_ynSES-qG9JyMFJltir^= z!o)zQ*?aT_oI=9G?-%}_-^JbSXZi7np5^mbp{x0%%=hiskP&jR<7j-1;P)Bg^QzbF 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