Electric Force: Difference between revisions

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--[[User:Asaxon7|Asaxon7]] ([[User talk:Asaxon7|talk]]) 00:48, 18 November 2015 (EST) Claimed by Alayna Saxon
== Claimed by Azan Khan — Fall 2025 ==


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


==The Coulomb Force Law==
== Key Concepts ==


The formula  for the magnitude of the electric force between two point charges is:
* 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).


<math>|\vec F|=\frac{1}{4 \pi \epsilon_0 } \frac{|{q}_{1}{q}_{2}|}{r^2} </math>
== Coulomb’s Law ==


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.
The electric force between two point charges is:


===Direction of Electric Force===
F = k * |q1 q2| / r^2


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.
where:


===Derivations of Electric Force===
F = electric force (Newtons)


The electric force on a particle can also be written as:
k = 8.99×10^9 N·m²/C² (Coulomb’s constant)


<math>\vec F=q\vec E </math>
q1, q2 = the two point charges


where '''<math>q</math>''' is the charge of the particle and '''<math>\vec E </math>''' is the external electric field.
r = distance between the charges


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:
== Vector Form of the Electric Force ==


<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>
Electric force has direction. The vector equation is:


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.
⃗F₁₂ = k * (q₁ q₂ / r²) * r̂₁₂


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


===Example 1===
== Common Misconceptions ==


'''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?
* 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.


'''Step 1: '''Find the distance between the two point charges.
== Real-World Examples ==


<math>d=\sqrt{(0 m-0 m)^2+(0 m-10 m)^2+(0 m-0 m)^2}=\sqrt{100 m}=10 </math>m.
* 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.


The distance between the two points is 10 m.
[[File:CoulombsLawDiagram.png|400px|thumb|Diagram of electric force between charges (public domain).]]


'''Step 2: '''Substitute values into the correct formula.
https://upload.wikimedia.org/wikipedia/commons/thumb/0/02/CoulombsLawDiagram.png/640px-CoulombsLawDiagram.png


<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>
== Interactive Simulation ==


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


<math>|\vec F|=4.5e-9 </math> N
<iframe src="https://trinket.io/embed/glowscript/31d0f9ad9e" width="100%" height="500"></iframe>


The magnitude of electric force is <math>|\vec F|=4.5e-9 </math> N.
Practice Problems


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


Since the first particle is positively charged and the second is negatively charged, the force is attractive. The particles are attracted to each other.
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


===Example 2===
== Sources ==


'''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.
* OpenStax University Physics (Public Domain)
 
* HyperPhysics (Public Domain)
'''Step 1: '''Substitute values into the correct formula.
* Wikimedia Commons (Public Domain Images)
 
<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.
 
==Connectedness==
#How is this topic connected to something that you are interested in?
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==History==
 
Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
 
== See also ==
 
Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?
 
===Further reading===
 
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===External links===
 
Internet resources on this topic
 
==References==
 
Matter & Interactions, Vol. II: Electric and Magnetic Interactions, 4th Edition
 
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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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