>[!summary]
>The electric force is an extension of [[Coulomb's Law]] and explains why a charged object will exert a force on another charged object.
>
Polarization:
A negative charged object close to a neutral charged object. Postive charges move in the direction of the negative object.
>
Induction:
If a neutral object is grounded and a charged object is brought close to that grounded object the neutral object will become oppositely charged if the grounded part is taken off.
>
Key equations:
$F = \frac{q q_2}{4\pi R^2 \epsilon _0}$
>[!info]+ Read Time
**⏱ 3 mins**
# What is The Electric Force
>[!warning]
The [[Electric Force]] and [[Electric Potential Energy]] are different
The electric force explains the interactions of a point charge in a [[Electric Field]]. **This is an extension of** [[Coulomb's Law]].
The electric force also explains how objects get charged by polarization or induction as a result of [[Coulomb's Law]] and why like charges repel. Denoted by the result you get after deriving the electric force
# Deriving The Electric Force
>[!warning] Assumptions
We will assume that a point charge will be in a electric field so that [[Dynamic Forces & Newtons Laws]] are true
>
We will assume:
Assume $F = q_1E$
Equations from [[Coulomb's Law]] are valid
![[el_2.png]]
[^2]
>[!note] Explanation
A point charge in a electric field.
$\begin{array}{c}
\text{A point charge is in a electric field, the force on the point charge is equal to} \\
F = q_1E \\
\\
\text{From Coulombs Law we know:} \\
E = \frac{q_2}{4\pi R^2 \epsilon _0} \\
\\
F = q(\frac{q_2}{4\pi R^2 \epsilon _0}) \\
F = \frac{q q_2}{4\pi R^2 \epsilon _0}
\end{array}$
# Polarization
If you have a negative charged object close to a neutral charged object. The neutral charged object will have some of its postive charges move in the direction of the negative charged object (Neg-pos attract).
>[!warning]
The charged particles will not jump to the other object in polarization.
![[Screenshot 2025-06-06 at 2.58.37 AM.png]]
[^1]
>[!note] Explanation
Example of polarization positive charges from the left object will be attracted to the right object negative charges.
>
No charges jump objects if they dont touch one another.
# Induction
Charging an object by induction is when you bring a charged object near a uncharged object, without touching one object to the other the like particles will be repelled and unlike particles will be attracted.
In this example you bring a negative charged object near a neutral cone, so the unlike charges are attracted to one another. The like charges repelsaway from one another.
![[Pasted image 20250601134835.png]]
If you now add another wire, the like charges want to as far away as possible form the unlike charges, and so take that path. One you remove the ground wire, the ground is now negatively charged and sphere is positive charged.
[^1]: Taken from https://tikz.net/charge/ by Izaak Neutelings (July 2018)
[^2]: Taken from https://tikz.net/electric_field/ by Izaak Neutelings (July 2018)
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