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E = | F q | = k | qQ qr 2 | = k | Q | r 2 . size 12{E= { {F} over {q} } =k { { ital "qQ"} over { ital "qr" rSup { size 8{2} } } } =k { {Q} over {r rSup { size 8{2} } } } } {}

Since the test charge cancels, we see that

E = k | Q | r 2 . size 12{E=k { {Q} over {r rSup { size 8{2} } } } } {}

The electric field is thus seen to depend only on the charge Q size 12{Q} {} and the distance r size 12{r} {} ; it is completely independent of the test charge q size 12{q} {} .

Calculating the electric field of a point charge

Calculate the strength and direction of the electric field E size 12{E} {} due to a point charge of 2.00 nC (nano-Coulombs) at a distance of 5.00 mm from the charge.

Strategy

We can find the electric field created by a point charge by using the equation E = kQ / r 2 size 12{E= { ital "kQ"} slash {r rSup { size 8{2} } } } {} .

Solution

Here Q = 2 . 00 × 10 9 size 12{Q=2 "." "00" times "10" rSup { size 8{ - 9} } } {} C and r = 5 . 00 × 10 3 size 12{r=5 "." "00" times "10" rSup { size 8{ - 3} } } {} m. Entering those values into the above equation gives

E = k Q r 2 = ( 8.99 × 10 9 N m 2 /C 2 ) × ( 2.00 × 10 9 C ) ( 5.00 × 10 3 m ) 2 = 7.19 × 10 5 N/C. alignl { stack { size 12{E=k { {Q} over {r rSup { size 8{2} } } } } {} #= \( 9 "." "00" times "10" rSup { size 8{9} } N cdot m rSup { size 8{2} } "/C" rSup { size 8{2} } \) times { { \( 2 "." "00" times "10" rSup { size 8{ - 9} } C \) } over { \( 5 "." "00" times "10" rSup { size 8{ - 3} } m \) rSup { size 8{2} } } } {} # =7 "." "20" times "10" rSup { size 8{5} } "N/C" {}} } {}

Discussion

This electric field strength is the same at any point 5.00 mm away from the charge Q size 12{Q} {} that creates the field. It is positive, meaning that it has a direction pointing away from the charge Q size 12{Q} {} .

Calculating the force exerted on a point charge by an electric field

What force does the electric field found in the previous example exert on a point charge of –0.250 μ C ?

Strategy

Since we know the electric field strength and the charge in the field, the force on that charge can be calculated using the definition of electric field E = F / q size 12{E= {F} slash {q} } {} rearranged to F = q E size 12{F= ital "qE"} {} .

Solution

The magnitude of the force on a charge q = 0 . 250 μC size 12{q= - 0 "." "250""μC"} {} exerted by a field of strength E = 7 . 20 × 10 5 size 12{E=7 "." "20" times "10" rSup { size 8{5} } } {} N/C is thus,

F = qE = ( 0.250 × 10 –6 C ) ( 7.20 × 10 5 N/C ) = 0.180 N. alignl { stack { size 12{F= ital "qE"} {} #size 12{ {}= \( "-0" "." "250" times "10" rSup { size 8{"-6"} } `C \) \( 7 "." "20" times "10" rSup { size 8{5} } `"N/C" \) } {} # ="-0" "." "180"`N {}} } {}

Because q is negative, the force is directed opposite to the direction of the field.

Discussion

The force is attractive, as expected for unlike charges. (The field was created by a positive charge and here acts on a negative charge.) The charges in this example are typical of common static electricity, and the modest attractive force obtained is similar to forces experienced in static cling and similar situations.

Section summary

  • The electrostatic force field surrounding a charged object extends out into space in all directions.
  • The electrostatic force exerted by a point charge on a test charge at a distance r size 12{r} {} depends on the charge of both charges, as well as the distance between the two.
  • The electric field E size 12{E} {} is defined to be
    E = F q , size 12{E= { {F} over {q,} } } {}

    where F size 12{F} {} is the Coulomb or electrostatic force exerted on a small positive test charge q size 12{q} {} . E size 12{E} {} has units of N/C.

  • The magnitude of the electric field E size 12{E} {} created by a point charge Q size 12{Q} {} is
    E = k | Q | r 2 . size 12{E=k { {Q} over {r rSup { size 8{2} } } } } {}

    where r size 12{r} {} is the distance from Q size 12{Q} {} . The electric field E size 12{E} {} is a vector and fields due to multiple charges add like vectors.

Conceptual questions

Why must the test charge q size 12{q} {} in the definition of the electric field be vanishingly small?

Are the direction and magnitude of the Coulomb force unique at a given point in space? What about the electric field?

Problem exercises

What is the magnitude and direction of an electric field that exerts a 2 . 00 × 10 - 5 N size 12{2 "." "00" times "10" rSup { size 8{5} } N} {} upward force on a –1.75 μ C charge?

What is the magnitude and direction of the force exerted on a 3.50 μ C charge by a 250 N/C electric field that points due east?

8 . 75 × 10 4 size 12{8 "." "75" times "10" rSup { size 8{ - 4} } } {} N

Calculate the magnitude of the electric field 2.00 m from a point charge of 5.00 mC (such as found on the terminal of a Van de Graaff).

(a) What magnitude point charge creates a 10,000 N/C electric field at a distance of 0.250 m? (b) How large is the field at 10.0 m?

(a) 6 . 94 × 10 8 C size 12{ {underline {6 "." "94" times "10" rSup { size 8{ - 8} } " C"}} } {}

(b) 6 . 25 N/C size 12{ {underline {6 "." "25"" N/C"}} } {}

Calculate the initial (from rest) acceleration of a proton in a 5 . 00 × 10 6 N/C size 12{5 "." "00" times "10" rSup { size 8{6} } "N/C"} {} electric field (such as created by a research Van de Graaff). Explicitly show how you follow the steps in the Problem-Solving Strategy for electrostatics.

(a) Find the direction and magnitude of an electric field that exerts a 4 . 80 × 10 17 N size 12{4 "." "80" times "10" rSup { size 8{ - "17"} } N} {} westward force on an electron. (b) What magnitude and direction force does this field exert on a proton?

(a) 300 N/C ( east ) size 12{ {underline {"300"" N/C " \( "eas"}} {underline {t \) }} } {}

(b) 4 . 80 × 10 17 N ( east ) size 12{ {underline {4 "." "80" times "10" rSup { size 8{ - "17"} } " N " \( "east" \) }} } {}

Questions & Answers

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
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
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
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
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Concepts of physics. OpenStax CNX. Aug 25, 2015 Download for free at https://legacy.cnx.org/content/col11738/1.5
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