Coulomb's law

Siyavula textbooks: grade 11 Page 1 / 2

Introduction

In Grade 10, you learnt about the force between charges. In this chapter you will learn exactly how to determine this force andabout a basic law of electrostatics.

Forces between charges - coulomb's law

Like charges repel each other while opposite charges attract each other. If the charges are at rest then the force between them is known as the electrostatic force . The electrostatic force between charges increases when the magnitudeof the charges increases or the distance between the charges decreases.

The electrostatic force was first studied in detail by Charles Coulomb around 1784. Through his observations he was ableto show that the electrostatic force between two point-like charges is inversely proportional to the square of the distancebetween the objects. He also discovered that the force is proportional to the product of the charges on the two objects. That is:

\begin{matrix} F \propto \frac{Q_{1} Q_{2}}{r^{2}}, \end{matrix}

where $Q_{1}$ is the charge on the one point-like object, $Q_{2}$ is the charge on the second, and $r$ is the distance between the two. The magnitude of the electrostatic force between two point-likecharges is given by Coulomb's Law .

Coulomb's Law

Coulomb's Law states that the magnitude of the electrostatic force between two point charges isdirectly proportional to the magnitudes of each charge and inversely proportional to the square of the distance between thecharges:

F = k \frac{Q_{1} Q_{2}}{r^{2}}

The proportionality constant $k$ is called the electrostatic constant and has the value:

k = 8, 99 \times 10^{9} N \cdot m^{2} \cdot C^{- 2} .

Similarity of coulomb's law to newton's universal law of gravitation.

Notice how similar Coulomb's Law is to the form of Newton's Universal Law of Gravitation between two point-likeparticles:

\begin{matrix} F_{G} = G \frac{m_{1} m_{2}}{r^{2}}, \end{matrix}

where $m_{1}$ and $m_{2}$ are the masses of the two particles, $r$ is the distance between them, and $G$ is the gravitational constant.

Both laws represent the force exerted by particles (masses or charges) on each other that interact by means of a field.

Khan academy video on electrostatics - 1

Two point-like charges carrying charges of $+ 3 \times 10^{- 9} C$ and $- 5 \times 10^{- 9} C$ are $2 m$ apart. Determine the magnitude of the force between them and state whether it isattractive or repulsive.

Determine what is required
We are required to find the force between two point charges given thecharges and the distance between them.
Determine how to approach the problem
We can use Coulomb's Law to find the force.

$F = k \frac{Q_{1} Q_{2}}{r^{2}}$
Determine what is given
We are given:
- $Q_{1} = + 3 \times 10^{- 9} C$
- $Q_{2} = - 5 \times 10^{- 9} C$
- $r = 2 m$
We know that $k = 8, 99 \times 10^{9} N \cdot m^{2} \cdot C^{- 2}$ .

We can draw a diagram of the situation.
Check units
All quantities are in SI units.
Determine the magnitude of the force
Using Coulomb's Law we have

$\begin{matrix} F & = & k \frac{Q_{1} Q_{2}}{r^{2}} \\ = & (8, 99 \times 10^{9} N \cdot m^{2} / C^{2}) \frac{(3 \times 10^{- 9} C) (5 \times 10^{- 9} C)}{{(2 m)}^{2}} \\ = & 3, 37 \times 10^{- 8} N \end{matrix}$

Thus the magnitude of the force is $3, 37 \times 10^{- 8} N$ . However since both point charges have opposite signs, the force will be attractive.

Got questions? Get instant answers now!

Next is another example that demonstrates the difference in magnitude between the gravitational force and the electrostaticforce.

Determine the electrostatic force and gravitational force between two electrons $10^{- 10} m$ apart (i.e. the forces felt inside an atom).

Determine what is required
We are required to calculate the electrostatic and gravitational forces between two electrons,a given distance apart.
Determine how to approach the problem
We can use:

$F_{e} = k \frac{Q_{1} Q_{2}}{r^{2}}$

to calculate the electrostatic force and

$F_{g} = G \frac{m_{1} m_{2}}{r^{2}}$

to calculate the gravitational force.
Determine what is given
- $Q_{1} = Q_{2} = 1, 6 \times 10^{- 19} C$ (The charge on an electron)
- $m_{1} = m_{2} = 9, 1 \times 10^{- 31} kg$ (The mass of an electron)
- $r = 1 \times 10^{- 10} m$
We know that:
- $k = 8, 99 \times 10^{9} N \cdot m^{2} \cdot C^{- 2}$
- $G = 6, 67 \times 10^{- 11} N \cdot m^{2} \cdot {kg}^{- 2}$
All quantities are in SI units.

We can draw a diagram of the situation.
Calculate the electrostatic force
$\begin{matrix} F_{e} & = & k \frac{Q_{1} Q_{2}}{r^{2}} \\ = & (8, 99 \times 10^{9}) \frac{(- 1, 60 \times 10^{- 19}) (- 1, 60 \times 10^{- 19})}{{(10^{- 10})}^{2}} \\ = & 2, 30 \times 10^{- 8} N \end{matrix}$

Hence the magnitude of the electrostatic force between the electrons is $2, 30 \times 10^{- 8} N$ . Since electrons carry the same charge, the force is repulsive.
Calculate the gravitational force
$\begin{matrix} F_{g} & = & G \frac{m_{1} m_{2}}{r^{2}} \\ = & (6, 67 \times 10^{- 11} N \cdot m^{2} / {kg}^{2}) \frac{(9.11 \times 10^{- 31} C) (9.11 \times 10^{- 31} kg)}{{(10^{- 10} m)}^{2}} \\ = & 5, 54 \times 10^{- 51} N \end{matrix}$

The magnitude of the gravitational force between the electrons is $5, 54 \times 10^{- 51} N$ . This is an attractive force.

Notice that the gravitational force between the electrons is much smaller than the electrostatic force. For this reason, thegravitational force is usually neglected when determining the force between two charged objects.

Got questions? Get instant answers now!

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?

Aislinn Reply

tijani

what is titration

John Reply

what is physics

Siyaka Reply

A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance

Jude Reply

Can you compute that for me. Ty

Jude

what is the dimension formula of energy?

David Reply

what is viscosity?

David

what is inorganic

emma Reply

what is chemistry

Youesf Reply

what is inorganic

emma

Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes

Adjei

please, I'm a physics student and I need help in physics

Adjanou

chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.

Pedro

A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity

Krampah Reply

2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.

Sahid Reply

you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s

Samuel Reply

can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?

Joseph Reply

Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time

Joseph

Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing

Joseph

"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true

Ryan

what's motion

Maurice Reply

what are the types of wave

Maurice

answer

Magreth

progressive wave

Magreth

hello friend how are you

Muhammad Reply

fine, how about you?

Mohammed

Mujahid

A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?

yasuo Reply

Who can show me the full solution in this problem?

Reofrir Reply

Got questions? Join the online conversation and get instant answers!

Jobilize.com Reply

<< Chapter < Page Page > Chapter >>

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

100% Free Mobile Applications
Receive real-time job alerts and never miss the right job again

Source: OpenStax, Siyavula textbooks: grade 11 physical science. OpenStax CNX. Jul 29, 2011 Download for free at http://cnx.org/content/col11241/1.2

Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Siyavula textbooks: grade 11 physical science' conversation and receive update notifications?

Ask

	Microeconomics Test 1 By IES Portal Start Test
©flickr: Gareth	Professional Etiquette MCQ By Abby Sharp Start Quiz
	9 BOD- Liver Quiz .... By Brooke Delaney Start Quiz
	13 Lec:13 Hypothesis Testing P-values By Janet Forrester Start Quiz
	1 Week 1 Social Psych By Yacoub Jayoghli Start Quiz
	15 Biology 15 Genes and Proteins MCQ By OpenStax Start Quiz
	14 AP 14 Brain Cranial Nerves MCQ By OpenStax Start Quiz
	5 Psychology MCQ 2010 1 Exam By John Gabrieli Start Exam
	20 Biology 20 Phylogenies the History of Life MCQ By OpenStax Start Quiz
	Autonomic Nervous System By Marriyam Rana Start Quiz