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This document is a compilation of my notes for COE 501: Electromagnetism: Theory and Effects at TMU. All information comes from my professor’s lectures, as well as the course textbook Elements of Electromagnetics, 7th Edition by Matthew Sadiku.
Adam Szava - 2tor.ca
F2022
This course is very heavy on the vector calculus. For this reason here we will review these parts of MTH312 here. Notes for this chapter will continue to be updated through the semester to reflect what is relevant to the course.
Recall that a vector is a linear combination of the basis vectors of it’s vector space. For example $\vec{v}=3\hat{a}_x+4\hat{a}_y-2\hat{a}_z$.
Here, $\hat{a}_i$ denotes the unit vector (length 1) in the $i$ direction.
Given two points $P_1$ and $P_2$, the unit vector connected them from $P_1$ to $P_2$ can be written as:
$$ \hat{a}{R{12}}=\frac{\vec{r}_2-\vec{r}_1}{|\vec{r}_2-\vec{r}_1|} $$
$\vec{r}$ denotes the position vector of a point, this position vector can be written in different ways depending on the coordinate system.
This chapter begins our basic study of electromagnetism with time-invariant fields in a vacuum.
Coulomb’s law experimentally related the electrostatic force between two charged particles to their charge, and the distance between them. Stated formally it is:
<aside> ➕ Definition 4.1 (Coulomb’s Law)
The force $F$ between two point charges $Q_1$ and $Q_2$ is:
As an equation this is (with proportionality constant $k=1/4\pi\varepsilon_0$):
$$ |\vec{F}|=\frac{Q_1Q_1}{4\pi\varepsilon_0R^2} $$
$$ \vec{F}{12}=\frac{Q_1Q_1}{4\pi\varepsilon_0R^2}\hat{a}{R_{12}} $$
$$ \vec{F}_{12}=\frac{Q_1Q_1(\vec{r_2}-\vec{r}_1)}{4\pi\varepsilon_0|\vec{r}_2-\vec{r}_1|^3} $$
</aside>
The constant $\varepsilon_0$ is defined as the permittivity of free space and is equal to:
$$ \varepsilon_0=8.854\times10^{-12}F/m $$