--[[User:Asaxon7|Asaxon7]] ([[User talk:Asaxon7|talk]]) 00:48, 18 November 2015 (EST) Claimed by Alayna Saxon
== Claimed by Azan Khan — Fall 2025 ==
claimed for editing and additional examples- Samuel Boyce Fall 2016
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]], and the strength of this electrical interaction is a vector quantity that has magnitude and direction. If the electric field at a particular location is known, then this field can be used to calculate the electric force of the particle being acted upon. The electric force is directly proportional to the amount of charge within each particle being acted upon by the other's electric field. Moreover, the magnitude of the force is inversely proportional to the square distance between the two interacting particles. It is important to remember that a particle cannot have an electric force on itself; there must be at least two interacting, charged components.
== Key Concepts ==
==The Main Idea==
* Like charges repel and opposite charges attract.
===A Mathematical Model===
* The electric force acts along the line connecting the two charges.
The Coulomb Force Law
* The magnitude of the force depends on the size of the charges and the distance between them.
The formula for the magnitude of the electric force between two point charges is:
* The force decreases with the square of the distance (inverse-square 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 expression <math>\frac{1}{4 \pi \epsilon_0 }</math> is known as the electric constant and carries the value 9e9.
The electric force between two point charges is:
Interestingly enough, one can see a relationship between this formula and the formula for gravitational force (<math>F={G} \frac{|{m}_{1}{m}_{2}|}{r^2} </math>). From this relationship, one can conclude that the interactions of two objects as a result of their charges or masses follow similar fundamental laws of physics.
F = k * |q1 q2| / r^2
'''Derivations of Electric Force'''
where:
The electric force on a particle can also be written as:
F = electric force (Newtons)
<math>\vec F=q\vec E </math>
k = 8.99×10^9 N·m²/C² (Coulomb’s constant)
where '''<math>q</math>''' is the charge of the particle and '''<math>\vec E </math>''' is the external electric field.
q1, q2 = the two point 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:
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.
Electric force has direction. The vector equation is:
⃗F₁₂ = k * (q₁ q₂ / r²) * r̂₁₂
===A Computational Model===
where r̂₁₂ represents a unit vector that points from the position of charge 1 to the position of charge 2.
Direction of the Electric Force
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. The electric force vector acts either in the same or opposite direction of the electric field acting on a particle, depending on the charge of that particle. Remember that negative charges attract, so the electric field of a negative charge will act from the observation location towards the charged negatively charged particle. If the observation particle is positively charged, then the electric force will act in the same direction as the electric field. If the observation particle is negatively charged, then the force will act in the opposite direction as the electric field. The same concepts apply to positive electric fields, which point away from the source location at the observation location.
[[File:WhatisAnElectricForce.png]]
== 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.
==Examples==
== Real-World Examples ==
===Simple===
* Static electricity on clothing is caused by attraction between oppositely charged areas.
'''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.
* Lightning forms when electric forces overcome air resistance.
* Electric forces guide the motion of electrons inside circuits.
'''Step 1: '''Substitute values into the correct formula.
[[File:CoulombsLawDiagram.png|400px|thumb|Diagram of electric force between charges (public domain).]]
'''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?
'''Step 1: '''Find the distance between the two point charges.
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.
The magnitude of electric force is <math>|\vec F|=4.5e-9 </math> N.
'''Step 3: '''Determine if force is attractive or repulsive.
Since the first particle is positively charged and the second is negatively charged, the force is attractive. The particles are attracted to each other.
===Difficult===
Problem:
[[File:SpringTest1Prob1.png]]
==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.
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.
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
