



$E=\left\frac{F}{q}\right=k\frac{\text{qQ}}{{\mathrm{qr}}^{2}}=k\frac{\leftQ\right}{{r}^{2}}.$
Since the test charge cancels, we see that
$E=k\frac{\leftQ\right}{{r}^{2}}.$
The electric field is thus seen to depend only on the charge
$Q$ and the distance
$r$ ; it is completely independent of the test charge
$q$ .
Calculating the electric field of a point charge
Calculate the strength and direction of the electric field
$E$ due to a point charge of 2.00 nC (nanoCoulombs) 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
$E=\text{kQ}/{r}^{2}$ .
Solution
Here
$Q=2\text{.}\text{00}\times {\text{10}}^{9}$ C and
$r=5\text{.}\text{00}\times {\text{10}}^{3}$ m. Entering those values into the above equation gives
$\begin{array}{lll}E& =& k\frac{Q}{{r}^{2}}\\ & =& (\text{8.99}\times {\text{10}}^{9}\phantom{\rule{0.25em}{0ex}}\text{N}\cdot {\text{m}}^{2}{\text{/C}}^{2})\times \frac{(\text{2.00}\times {\text{10}}^{9}\phantom{\rule{0.25em}{0ex}}\text{C})}{(\text{5.00}\times {\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{m}{)}^{2}}\\ & =& \text{7.19}\times {\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}\text{N/C.}\end{array}$
Discussion
This
electric field strength is the same at any point 5.00 mm away from the charge
$Q$ that creates the field. It is positive, meaning that it has a direction pointing away from the charge
$Q$ .
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
$\mathrm{\u20130.250}\phantom{\rule{0.25em}{0ex}}\mu \text{C}$ ?
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
$\mathbf{\text{E}}=\mathbf{\text{F}}/q$ rearranged to
$\mathbf{\text{F}}=q\mathbf{\text{E}}$ .
Solution
The magnitude of the force on a charge
$q=0\text{.}\text{250}\phantom{\rule{0.25em}{0ex}}\text{\mu C}$ exerted by a field of strength
$E=7\text{.}\text{20}\times {\text{10}}^{5}$ N/C is thus,
$\begin{array}{lll}F& =& \text{qE}\\ & =& (\text{0.250}\times {\text{10}}^{\text{\u20136}}\phantom{\rule{0.25em}{0ex}}\text{C})(7.20\times {\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}\text{N/C})\\ & =& \text{0.180 N.}\end{array}$
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
$r$ depends on the charge of both charges, as well as the distance between the two.
 The electric field
$\mathbf{\text{E}}$ is defined to be
$\mathbf{\text{E}}=\frac{\mathbf{\text{F}}}{q,}$
where
$\mathbf{\text{F}}$ is the Coulomb or electrostatic force exerted on a small positive test charge
$q$ .
$\mathbf{\text{E}}$ has units of N/C.
 The magnitude of the electric field
$\mathbf{\text{E}}$ created by a point charge
$Q$ is
$\mathbf{\text{E}}=k\frac{\leftQ\right}{{r}^{2}}.$
where
$r$ is the distance from
$Q$ . The electric field
$\mathbf{\text{E}}$ is a vector and fields due to multiple charges add like vectors.
Conceptual questions
Why must the test charge
$q$ 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
$2\text{.}\text{00}\times {\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}\text{N}$ upward force on a
$\mathrm{\u20131.75}\phantom{\rule{0.25em}{0ex}}\mu \text{C}$ charge?
What is the magnitude and direction of the force exerted on a
$3.50\phantom{\rule{0.25em}{0ex}}\mu \text{C}$ charge by a 250 N/C electric field that points due east?
$8\text{.}\text{75}\times {\text{10}}^{4}$ 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)
$6\text{.}\text{94}\times {\text{10}}^{8}\phantom{\rule{0.25em}{0ex}}\text{C}$
(b)
$6\text{.}\text{25}\phantom{\rule{0.25em}{0ex}}\text{N/C}$
Calculate the initial (from rest) acceleration of a proton in a
$5\text{.}\text{00}\times {\text{10}}^{6}\phantom{\rule{0.25em}{0ex}}\text{N/C}$ electric field (such as created by a research Van de Graaff). Explicitly show how you follow the steps in the ProblemSolving Strategy for electrostatics.
(a) Find the direction and magnitude of an electric field that exerts a
$4\text{.}\text{80}\times {\text{10}}^{\text{17}}\phantom{\rule{0.25em}{0ex}}\text{N}$ westward force on an electron. (b) What magnitude and direction force does this field exert on a proton?
(a)
$\text{300}\phantom{\rule{0.25em}{0ex}}\text{N/C}\phantom{\rule{0.25em}{0ex}}(\text{east})$
(b)
$4\text{.}\text{80}\times {\text{10}}^{\text{17}}\phantom{\rule{0.25em}{0ex}}\text{N}\phantom{\rule{0.25em}{0ex}}(\text{east})$
Questions & Answers
anyone know any internet site where one can find nanotechnology papers?
Introduction about quantum dots in nanotechnology
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?
how to know photocatalytic properties of tio2 nanoparticles...what to do now
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
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
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
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials and their applications of sensors.
Difference between extinct and extici spicies
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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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