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  • 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.

Questions & Answers

what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Physics 105: adventures in physics. OpenStax CNX. Dec 02, 2015 Download for free at http://legacy.cnx.org/content/col11916/1.1
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