ece106: add electric fields

docs/1b/ece106.md

@@ -170,6 +170,12 @@ Please see [SL Physics 1#Charge](/sph3u7/#charge) for more information.
 
 $$\vec F_{12}=k\frac{Q_1Q_2}{||R_{12}||^2}\hat{R_{12}}$$
 
+!!! warning
+    Because Coulomb's law is an experimental law, it does not quite cover all of the nuances of electrostatics. Notably:
+    
+    - $Q_1$ and $Q_2$ must be point charges, making distributed charges inefficient to calculate, and
+    - the formula breaks down once charges begin to move (e.g., if a charge moves a lightyear away from another, Coulomb's law says the force changes instantly. In reality, it takes a year before the other charge observes a difference.)
+
 ### Dipoles
 
 An **electric dipole** is composed of two equal but opposite charges $Q$ separated by a distance $d$. The dipole moment is the product of the two, $Qd$.
@@ -177,3 +183,10 @@ An **electric dipole** is composed of two equal but opposite charges $Q$ separat
 The charge experienced by a positive test charge along the dipole line can be reduced to:
 $$\vec F_q=\hat x\frac{2kQdq}{||\vec x||^3}$$
 
+### Maxwell's theorems
+
+Compared to Coulomb's law, $Q_1$ creates an electric field around itself — each point in space is assigned a vector that depends on the distance away from the charge. $Q_2$ *interacts* with the field. According to Maxwell, as a charge moves, it emits a wave that carries information to other charges.
+
+The **electric field strength** $\vec E$ is the force per unit *positive* charge at a specific point:
+
+$$\vec E=\frac{\vec{F}}{q}$$