1. Home
  2. College physics
  3. Electric charge and electric
  4. Coulomb’s law

18.3 Coulomb’s law

<< Chapter < Page
  College physics     Page 1 / 6
Chapter >> Page >
  • State Coulomb’s law in terms of how the electrostatic force changes with the distance between two objects.
  • Calculate the electrostatic force between two charged point forces, such as electrons or protons.
  • Compare the electrostatic force to the gravitational attraction for a proton and an electron; for a human and the Earth.
Two spiral galaxies show the strong gravitational attraction between them as their arms appear to reach out toward one another.
This NASA image of Arp 87 shows the result of a strong gravitational attraction between two galaxies. In contrast, at the subatomic level, the electrostatic attraction between two objects, such as an electron and a proton, is far greater than their mutual attraction due to gravity. (credit: NASA/HST)

Through the work of scientists in the late 18th century, the main features of the electrostatic force    —the existence of two types of charge, the observation that like charges repel, unlike charges attract, and the decrease of force with distance—were eventually refined, and expressed as a mathematical formula. The mathematical formula for the electrostatic force is called Coulomb’s law    after the French physicist Charles Coulomb (1736–1806), who performed experiments and first proposed a formula to calculate it.

Coulomb’s law

F = k | q 1 q 2 | r 2 . size 12{F=k { {q rSub { size 8{1} } q rSub { size 8{2} } } over {r rSup { size 8{2} } } } } {}

Coulomb’s law calculates the magnitude of the force F between two point charges, q 1 size 12{q rSub { size 8{1} } } {} and q 2 size 12{q rSub { size 8{2} } } {} , separated by a distance r . In SI units, the constant k is equal to

k = 8 . 988 × 10 9 N ⋅ m 2 C 2 ≈ 8 . 99 × 10 9 N ⋅ m 2 C 2 . size 12{k=8 "." "988" times "10" rSup { size 8{9} } { {N cdot m rSup { size 8{2} } } over {C rSup { size 8{2} } } } approx 9 "." "00" times "10" rSup { size 8{9} } { {N cdot m rSup { size 8{2} } } over {C rSup { size 8{2} } } } } {}

The electrostatic force is a vector quantity and is expressed in units of newtons. The force is understood to be along the line joining the two charges. (See [link] .)

Although the formula for Coulomb’s law is simple, it was no mean task to prove it. The experiments Coulomb did, with the primitive equipment then available, were difficult. Modern experiments have verified Coulomb’s law to great precision. For example, it has been shown that the force is inversely proportional to distance between two objects squared F ∝ 1 / r 2 size 12{ left (F prop {1} slash {r rSup { size 8{2} } } right )} {} to an accuracy of 1 part in 10 16 size 12{"10" rSup { size 8{"16"} } } {} . No exceptions have ever been found, even at the small distances within the atom.

In part a, two charges q one and q two are shown at a distance r. Force vector arrow F one two points toward left and acts on q one. Force vector arrow F two one points toward right and acts on q two. Both forces act in opposite directions and are represented by arrows of same length. In part b, two charges q one and q two are shown at a distance r. Force vector arrow F one two points toward right and acts on q one. Force vector arrow F two one points toward left and acts on q two. Both forces act toward each other and are represented by arrows of same length.
The magnitude of the electrostatic force F size 12{F} {} between point charges q 1 size 12{q rSub { size 8{1} } } {} and q 2 size 12{q rSub { size 8{2} } } {} separated by a distance r size 12{F} {} is given by Coulomb’s law. Note that Newton’s third law (every force exerted creates an equal and opposite force) applies as usual—the force on q 1 size 12{q rSub { size 8{1} } } {} is equal in magnitude and opposite in direction to the force it exerts on q 2 size 12{q rSub { size 8{2} } } {} . (a) Like charges. (b) Unlike charges.

How strong is the coulomb force relative to the gravitational force?

Compare the electrostatic force between an electron and proton separated by 0 . 530 × 10 − 10 m size 12{0 "." "530" times "10" rSup { size 8{ - "10"} } m} {} with the gravitational force between them. This distance is their average separation in a hydrogen atom.

Strategy

To compare the two forces, we first compute the electrostatic force using Coulomb’s law, F = k | q 1 q 2 | r 2 size 12{F=k { {q rSub { size 8{1} } q rSub { size 8{2} } } over {r rSup { size 8{2} } } } } {} . We then calculate the gravitational force using Newton’s universal law of gravitation. Finally, we take a ratio to see how the forces compare in magnitude.

Solution

Entering the given and known information about the charges and separation of the electron and proton into the expression of Coulomb’s law yields

F = k | q 1 q 2 | r 2 size 12{F=k { {q rSub { size 8{1 } } q rSub { size 8{2} } } over {r rSup { size 8{2} } } } } {}
= 8.99 × 10 9 N ⋅ m 2 / C 2 × ( 1.60 × 10 –19 C ) ( 1.60 × 10 –19 C ) ( 0.530 × 10 –10 m ) 2 alignl { stack { size 12{" "= left (9 "." "00 " times " 10" rSup { size 8{9} } N cdot " m" rSup { size 8{2} } /C rSup { size 8{2} } right ) times { { \( "-1" "." "60 " times " 10" rSup { size 8{"-19"} } C \) \( 1 "." "60" times " 10" rSup { size 8{"-19 "} } C \) } over { \( 0 "." "530 " times " 10" rSup { size 8{"-10"} } m \) rSup { size 8{2} } } } } {} #{} } } {}

Thus the Coulomb force is

F = 8.19 × 10 –8 N . size 12{F=" -8" "." "20 " times " 10" rSup { size 8{"-8"} } N} {}

The charges are opposite in sign, so this is an attractive force. This is a very large force for an electron—it would cause an acceleration of 8.99 × 10 22 m / s 2 size 12{9 "." "00" times "10" rSup { size 8{"22"} } {m} slash {s rSup { size 8{2} } } } {} (verification is left as an end-of-section problem).The gravitational force is given by Newton’s law of gravitation as:

F G = G mM r 2 , size 12{F rSub { size 8{G} } =" G " { {"mM"} over {r rSup { size 8{2} } } } } {}

where G = 6.67 × 10 − 11 N ⋅ m 2 / kg 2 size 12{G=6 "." "67" times "10" rSup { size 8{ - "11"} } {N cdot m rSup { size 8{2} } } slash { ital "kg" rSup { size 8{2} } } } {} . Here m and M represent the electron and proton masses, which can be found in the appendices. Entering values for the knowns yields

F G = ( 6.67 × 10 – 11 N ⋅ m 2 / kg 2 ) × ( 9.11 × 10 –31 kg ) ( 1.67 × 10 –27 kg ) ( 0.530 × 10 –10 m ) 2 = 3.61 × 10 –47 N

This is also an attractive force, although it is traditionally shown as positive since gravitational force is always attractive. The ratio of the magnitude of the electrostatic force to gravitational force in this case is, thus,

F F G = 2 . 27 × 10 39 . size 12{ { {F} over {F rSub { size 8{G} } } } =" 2" "." "27 " times " 10" rSup { size 8{"39"} } } {}

Discussion

This is a remarkably large ratio! Note that this will be the ratio of electrostatic force to gravitational force for an electron and a proton at any distance (taking the ratio before entering numerical values shows that the distance cancels). This ratio gives some indication of just how much larger the Coulomb force is than the gravitational force between two of the most common particles in nature.

Got questions? Get instant answers now!

Questions & Answers

how do you get the 2/50
Abba Reply
number of sport play by 50 student construct discrete data
Aminu Reply
width of the frangebany leaves on how to write a introduction
Theresa Reply
Solve the mean of variance
Veronica Reply
Step 1: Find the mean. To find the mean, add up all the scores, then divide them by the number of scores. ... Step 2: Find each score's deviation from the mean. ... Step 3: Square each deviation from the mean. ... Step 4: Find the sum of squares. ... Step 5: Divide the sum of squares by n – 1 or N.
kenneth
what is error
Yakuba Reply
Is mistake done to something
Vutshila
Hy
anas
hy
What is the life teble
anas
hy
Jibrin
statistics is the analyzing of data
Tajudeen Reply
what is statics?
Zelalem Reply
how do you calculate mean
Gloria Reply
diveving the sum if all values
Shaynaynay
let A1,A2 and A3 events be independent,show that (A1)^c, (A2)^c and (A3)^c are independent?
Fisaye Reply
what is statistics
Akhisani Reply
data collected all over the world
Shaynaynay
construct a less than and more than table
Imad Reply
The sample of 16 students is taken. The average age in the sample was 22 years with astandard deviation of 6 years. Construct a 95% confidence interval for the age of the population.
Aschalew Reply
Bhartdarshan' is an internet-based travel agency wherein customer can see videos of the cities they plant to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400 a. what is the probability of getting more than 12,000 hits? b. what is the probability of getting fewer than 9,000 hits?
Akshay Reply
Bhartdarshan'is an internet-based travel agency wherein customer can see videos of the cities they plan to visit. The number of hits daily is a normally distributed random variable with a mean of 10,000 and a standard deviation of 2,400. a. What is the probability of getting more than 12,000 hits
Akshay
1
Bright
Sorry i want to learn more about this question
Bright
Someone help
Bright
a= 0.20233 b=0.3384
Sufiyan
a
Shaynaynay
How do I interpret level of significance?
Mohd Reply
It depends on your business problem or in Machine Learning you could use ROC- AUC cruve to decide the threshold value
Shivam
how skewness and kurtosis are used in statistics
Owen Reply
yes what is it
Taneeya
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>
Practice Key Terms 3

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask