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'''CLAIMED BY AMARACHI EZE: MARCH 19, 2016'''
== Claimed by Azan Khan — Fall 2025 ==


--[[User:Asaxon7|Asaxon7]] ([[User talk:Asaxon7|talk]]) 00:48, 18 November 2015 (EST) Claimed by Alayna Saxon
Introduction:
The electric force is one of the four fundamental interactions of nature. It describes how charged objects push or pull on each other. This page explains the physical meaning of electric force, how to calculate it using Coulomb’s Law, and how the force behaves in real-world situations. The goal is to give students an intuitive and mathematical understanding of the concept as used in Physics 2.


This page contains information on the electric force on a point charge. Electric force is created by an external [[Electric Field]].
== Key Concepts ==


==The Coulomb Force Law==
* Like charges repel and opposite charges attract.
* The electric force acts along the line connecting the two charges.
* The magnitude of the force depends on the size of the charges and the distance between them.
* The force decreases with the square of the distance (inverse-square law).


The formula  for the magnitude of the electric force between two point charges is:
== Coulomb’s Law ==


<math>|\vec F|=\frac{1}{4 \pi \epsilon_0 } \frac{|{q}_{1}{q}_{2}|}{r^2} </math>
The electric force between two point charges is:


where '''<math>{q}_{1}</math>''' and '''<math>{q}_{2}</math>''' are the magnitudes of charge of point 1 and point 2 and '''<math>r</math>''' is the distance between the two point charges. The units for electric force are in Newtons.
F = k * |q1 q2| / r^2


===Direction of Electric Force===
where:


The electric force is along a straight line between the two point charges in the observed system. If the point charges have the same sign (i.e. both are either positively or negatively charged), then the charges repel each other. If the signs of the point charges are different (i.e. one is positively charged and one is negatively charged), then the point charges are attracted to each other.
F = electric force (Newtons)


===Derivations of Electric Force===
k = 8.99×10^9 N·m²/C² (Coulomb’s constant)


The electric force on a particle can also be written as:
q1, q2 = the two point charges


<math>\vec F=q\vec E </math>
r = distance between the charges


where '''<math>q</math>''' is the charge of the particle and '''<math>\vec E </math>''' is the external electric field.
== Vector Form of the Electric Force ==


This formula can be derived from <math>|\vec F|=\frac{1}{4 \pi \epsilon_0 } \frac{|{q}_{1}{q}_{2}|}{r^2} </math>, the electric force between two point charges. The magnitude of the electric field created by a point charge is <math>|\vec E|=\frac{1}{4 \pi \epsilon_0 } \frac{|q|}{r^2} </math>, where '''<math>q</math>''' is the magnitude of the charge of the particle and '''<math>r</math>''' is the distance between the observation location and the point charge. Therefore, the magnitude of electric force between point charge 1 and point charge 2 can be written as:
Electric force has direction. The vector equation is:


<math>|\vec F|=\frac{1}{4 \pi \epsilon_0 } \frac{|{q}_{1}{q}_{2}|}{r^2}=|{q}_{2}|\frac{1}{4 \pi \epsilon_0 } \frac{|{q}_{1}|}{r^2}=|{q}_{2}||\vec{E}_{1}| </math>
⃗F₁₂ = k * (q₁ q₂ / r²) * r̂₁₂


The units of charge are in Coulombs and the units for electric field are in Newton/Coulombs, so this derivation is correct in its dimensions since multiplying the two units gives just Newtons. The Newton is the unit for electric force.
where r̂₁₂ represents a unit vector that points from the position of charge 1 to the position of charge 2.


==A Computational Model==
== Common Misconceptions ==


==Examples==
* The electric force is NOT zero just because the net charge is zero.
* The force is not "shared" between charges — each charge experiences its own force.
* Coulomb’s Law applies only to point charges or spherically symmetric charge distributions.


===Example 1===
== Real-World Examples ==


'''Problem: '''Find the magnitude of electric force on two charged particles located at <math> <0, 0, 0></math>m and <math> <0, 10, 0></math>m. The first particle has a charge of +5 nC and the second particle has a charge of -10 nC. Is the force attractive or repulsive?
* Static electricity on clothing is caused by attraction between oppositely charged areas.
* Lightning forms when electric forces overcome air resistance.
* Electric forces guide the motion of electrons inside circuits.


'''Step 1: '''Find the distance between the two point charges.
[[File:CoulombsLawDiagram.png|400px|thumb|Diagram of electric force between charges (public domain).]]


<math>d=\sqrt{(0 m-0 m)^2+(0 m-10 m)^2+(0 m-0 m)^2}=\sqrt{100 m}=10 </math>m.
https://upload.wikimedia.org/wikipedia/commons/thumb/0/02/CoulombsLawDiagram.png/640px-CoulombsLawDiagram.png


The distance between the two points is 10 m.
== Interactive Simulation ==


'''Step 2: '''Substitute values into the correct formula.
Below is a GlowScript model showing the electric force between two charges.


<math>|\vec F|=\frac{1}{4 \pi \epsilon_0 } \frac{|{q}_{1}{q}_{2}|}{r^2}=\frac{1}{4 \pi \epsilon_0 } \frac{|(5 nC)(-10 nC)|}{(10m)^2} </math>
<iframe src="https://trinket.io/embed/glowscript/31d0f9ad9e" width="100%" height="500"></iframe>


Practice Problems


<math>|\vec F|=4.5e-9 </math> N
Problem 1:
Two charges of +3 μC and –2 μC are separated by 0.40 m. Find the magnitude of the electric force between them.
F = k * |q1 q2| / r^2
F = (8.99×10^9) * (3×10^-6)(2×10^-6) / (0.40)^2
F = 0.34 N


The magnitude of electric force is <math>|\vec F|=4.5e-9 </math> N.
Problem 2:
Two electrons are separated by 1 nm. What is the electric force between them?
F = k * e^2 / r^2
F = (8.99×10^9) * (1.6×10^-19)^2 / (1×10^-9)^2
F = 2.3×10^-10 N


'''Step 3: '''Determine if force is attractive or repulsive.
== Sources ==


Since the first particle is positively charged and the second is negatively charged, the force is attractive. The particles are attracted to each other.
* OpenStax University Physics (Public Domain)
 
* HyperPhysics (Public Domain)
===Example 2===
* Wikimedia Commons (Public Domain Images)
 
'''Problem: '''Find the electric force of a -3 C particle in a region with an electric field of <math><7, 5, 0></math>N/C.
 
'''Step 1: '''Substitute values into the correct formula.
 
<math>\vec F=q\vec E </math>
 
<math>\vec F=(-3 C)<7, 5, 0></math>N/C
 
<math>\vec F=<-21, -15, 0></math>N
 
The electric force vector for this particle is <math><-21, -15, 0></math>N.
 
===Example 3===
 
==Connectedness==
 
==History==
 
French physicist Charles-Augustin de Coulomb discovered in 1785 that the magnitude of electric force between two charged particles is directly proportional to the product of the absolute value of the two charges and inversely proportional to the distance squared between the two particles. He experimented with a torsion balance which consisted of an insulated bar suspended in the air by a silk thread. Coulomb attached a metal ball with a known charge to one end of the insulated bar. He then brought another ball with the same charge near the first ball. This distance between the two balls was recorded. The balls repelled each other, causing the silk thread to twist. The angle of the twist was measured and by knowing how much force was required for the thread to twist through the recorded angle, Coulomb was able to calculate the force between the two balls and derive the formula for electric force.
 
== See also ==
 
===External links===
 
http://www.physicsclassroom.com/class/estatics/Lesson-3/Coulomb-s-Law
 
==References==
 
Matter & Interactions, Vol. II: Electric and Magnetic Interactions, 4th Edition
 
https://en.wikipedia.org/wiki/Coulomb's_law
 
[[Category:Which Category did you place this in?]]

Latest revision as of 11:32, 28 November 2025

Claimed by Azan Khan — Fall 2025

Introduction: The electric force is one of the four fundamental interactions of nature. It describes how charged objects push or pull on each other. This page explains the physical meaning of electric force, how to calculate it using Coulomb’s Law, and how the force behaves in real-world situations. The goal is to give students an intuitive and mathematical understanding of the concept as used in Physics 2.

Key Concepts

  • Like charges repel and opposite charges attract.
  • The electric force acts along the line connecting the two charges.
  • The magnitude of the force depends on the size of the charges and the distance between them.
  • The force decreases with the square of the distance (inverse-square law).

Coulomb’s Law

The electric force between two point charges is:

F = k * |q1 q2| / r^2

where:

F = electric force (Newtons)

k = 8.99×10^9 N·m²/C² (Coulomb’s constant)

q1, q2 = the two point charges

r = distance between the charges

Vector Form of the Electric Force

Electric force has direction. The vector equation is:

⃗F₁₂ = k * (q₁ q₂ / r²) * r̂₁₂ 

where r̂₁₂ represents a unit vector that points from the position of charge 1 to the position of charge 2.

Common Misconceptions

  • The electric force is NOT zero just because the net charge is zero.
  • The force is not "shared" between charges — each charge experiences its own force.
  • Coulomb’s Law applies only to point charges or spherically symmetric charge distributions.

Real-World Examples

  • Static electricity on clothing is caused by attraction between oppositely charged areas.
  • Lightning forms when electric forces overcome air resistance.
  • Electric forces guide the motion of electrons inside circuits.
File:CoulombsLawDiagram.png
Diagram of electric force between charges (public domain).

https://upload.wikimedia.org/wikipedia/commons/thumb/0/02/CoulombsLawDiagram.png/640px-CoulombsLawDiagram.png

Interactive Simulation

Below is a GlowScript model showing the electric force between two charges.

<iframe src="https://trinket.io/embed/glowscript/31d0f9ad9e" width="100%" height="500"></iframe>

Practice Problems

Problem 1: Two charges of +3 μC and –2 μC are separated by 0.40 m. Find the magnitude of the electric force between them. F = k * |q1 q2| / r^2 F = (8.99×10^9) * (3×10^-6)(2×10^-6) / (0.40)^2 F = 0.34 N

Problem 2: Two electrons are separated by 1 nm. What is the electric force between them? F = k * e^2 / r^2 F = (8.99×10^9) * (1.6×10^-19)^2 / (1×10^-9)^2 F = 2.3×10^-10 N

Sources

  • OpenStax University Physics (Public Domain)
  • HyperPhysics (Public Domain)
  • Wikimedia Commons (Public Domain Images)
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