36 lines
2.5 KiB
Markdown
36 lines
2.5 KiB
Markdown
# Electric Charge
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- Charges come in two varieties, positive and negative.
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- Net charge is the *algebraic sum* of an object's charges
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- Protons and electrons have the same magnitude of charge (designated $1e$; a unit, **not** Euler's number)
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- The SI Unit of charge is the *Coulomb* (abbreviated C)
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- The smallest discrete quantity of charge is $\frac{1}{3}e$.
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- In an isolated system, the net charge will always remain constant.
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# Coulomb's Law
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- Two charges will exert a force on each other along the line joining them.
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- The magnitude of this force is proportional to the *product of the charges* and inversely proportional to the to the $\sqrt{dist}$.
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- The equation to determine the force between two charges is as follows:
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$$ \vec{F}_{12} = \vec{r}k\frac{q_1q_2}{r^2} $$
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- $\vec{r}$ is a unit vector pointing from charge 1 to charge 2
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- $k$ is Coulomb's constant, or $8.99 * 10^9 \frac{Nm^2}{C^2}$
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- $q_1$ and $q_2$ are the charges
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- $r$ is the distance between those charges
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- The resulting force will push away if $q_1q_2$ is *positive*, and attract if $q_1q_2$ is negative. This is where the rule "opposites attract, like repels" comes from
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- Coulomb's law only holds exactly true for *point charges* i.e a proton or electron.
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# The Superposition Principle
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The superposition principle states that:
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> The net force acting on a point charge is equal to the sum of all individual forces.
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This means that to find the net force acting on a single charge, you add up all of the individual forces acting on that charge.
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# The Electric Dipole
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An electric dipole consists of two point charges of equal magnitude but opposite sign. Many molecules behave like dipoles.
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- **Electric dipole moment** ($p$) is defined as the product of the charge $q$ and the separation $d$ between the two charges making up the dipole. $p = qd$
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- The dipole field at large distances decreases as the inverse *cube* of the distance. This is because the dipole has zero *net* charge.
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# Continuous Charge Distributions
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It's largely impossible to sum the electric field from every particle in a piece of matter, so the approximation is made that the charge is spread continuously over the distribution.
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- If the charge distribution extends throughout a *3d volume*, we describe it in terms of the **volume charge density** $\rho$, with units of $\frac{C}{m^3}$.
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- For charge distributions spread over *surfaces*, we use **surface charge density** $\sigma$ ($\frac{C}{m^2}$).
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- For charge distributions spread over *lines*, we use **line charge density** $\lambda$ ($\frac{C}{m}$). |