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(a) Using the symmetry of the arrangement, show that the electric field at the center of the square in [link] is zero if the charges on the four corners are exactly equal. (b) Show that this is also true for any combination of charges in which q a = q d size 12{q rSub { size 8{a} } =q rSub { size 8{d} } } {} and q b = q c size 12{q rSub { size 8{b} } =q rSub { size 8{z} } } {}

(a) What is the direction of the total Coulomb force on q size 12{q} {} in [link] if q size 12{q} {} is negative, q a = q c size 12{q rSub { size 8{a} } =q rSub { size 8{c} } } {} and both are negative, and q b = q c size 12{q rSub { size 8{b} } =q rSub { size 8{c} } } {} and both are positive? (b) What is the direction of the electric field at the center of the square in this situation?

Considering [link] , suppose that q a = q d size 12{q rSub { size 8{a} } =q rSub { size 8{d} } } {} and q b = q c size 12{q rSub { size 8{b} } =q rSub { size 8{c} } } {} . First show that q size 12{q} {} is in static equilibrium. (You may neglect the gravitational force.) Then discuss whether the equilibrium is stable or unstable, noting that this may depend on the signs of the charges and the direction of displacement of q size 12{q} {} from the center of the square.

If q a = 0 size 12{q rSub { size 8{a} } =0} {} in [link] , under what conditions will there be no net Coulomb force on q size 12{q} {} ?

In regions of low humidity, one develops a special “grip” when opening car doors, or touching metal door knobs. This involves placing as much of the hand on the device as possible, not just the ends of one’s fingers. Discuss the induced charge and explain why this is done.

Tollbooth stations on roadways and bridges usually have a piece of wire stuck in the pavement before them that will touch a car as it approaches. Why is this done?

Suppose a woman carries an excess charge. To maintain her charged status can she be standing on ground wearing just any pair of shoes? How would you discharge her? What are the consequences if she simply walks away?

Problems&Exercises

Sketch the electric field lines in the vicinity of the conductor in [link] given the field was originally uniform and parallel to the object’s long axis. Is the resulting field small near the long side of the object?

A oblong-shaped conductor.

Sketch the electric field lines in the vicinity of the conductor in [link] given the field was originally uniform and parallel to the object’s long axis. Is the resulting field small near the long side of the object?

A oblong-shaped conductor.

Sketch the electric field between the two conducting plates shown in [link] , given the top plate is positive and an equal amount of negative charge is on the bottom plate. Be certain to indicate the distribution of charge on the plates.

Two plates are shown; one is in horizontal direction and other is above the first plate with some inclination.

Sketch the electric field lines in the vicinity of the charged insulator in [link] noting its nonuniform charge distribution.

A positively charged rod with a concentration of positive charges near the top and a few in the middle.
A charged insulating rod such as might be used in a classroom demonstration.

What is the force on the charge located at x = 8.00 cm in [link] (a) given that q = 1 . 00 μC size 12{q=1 "." "00""μC"} {} ?

Three point charges are shown on the scaling line. First charge plus q is at three point zero, second charge minus two q is at eight point zero, and third charge plus q is eleven point zero centimeters along the x axis. Four charges are placed on a scaling line. First is minus two q at one point zero, second is plus q at five point zero, third is plus three q is at eight point zero, and fourth is minus q placed at fourteen point zero centimeter along the x axis.
(a) Point charges located at 3.00, 8.00, and 11.0 cm along the x -axis. (b) Point charges located at 1.00, 5.00, 8.00, and 14.0 cm along the x -axis.

(a) Find the total electric field at x = 1.00 cm in [link] (b) given that q = 5.00 nC . (b) Find the total electric field at x = 11.00 cm in [link] (b). (c) If the charges are allowed to move and eventually be brought to rest by friction, what will the final charge configuration be? (That is, will there be a single charge, double charge, etc., and what will its value(s) be?)

(a) E x = 1.00 cm = size 12{E rSub { size 8{x=1 "." "00" ital "cm"} } = - infinity } {}

(b) 2 . 12 × 10 5 N/C size 12{ {underline {2 "." "12" times "10" rSup { size 8{5} } " N/C" {underline {}} }} } {}

(c) one charge of + q

(a) Find the electric field at x = 5.00 cm in [link] (a), given that q = 1.00 μC size 12{q=1 "." "00""μC"} {} . (b) At what position between 3.00 and 8.00 cm is the total electric field the same as that for –2 q alone? (c) Can the electric field be zero anywhere between 0.00 and 8.00 cm? (d) At very large positive or negative values of x , the electric field approaches zero in both (a) and (b). In which does it most rapidly approach zero and why? (e) At what position to the right of 11.0 cm is the total electric field zero, other than at infinity? (Hint: A graphing calculator can yield considerable insight in this problem.)

(a) Find the total Coulomb force on a charge of 2.00 nC located at x = 4.00 cm in [link] (b), given that q = 1.00 μC size 12{q=1 "." "00""μC"} {} . (b) Find the x -position at which the electric field is zero in [link] (b).

(a) 0.252 N to the left

(b) x = 6.07 cm

Using the symmetry of the arrangement, determine the direction of the force on q size 12{q} {} in the figure below, given that q a = q b =+ 7 . 50 μC size 12{q rSub { size 8{a} } =q rSub { size 8{b} } "=+"7 "." "50""μC"} {} and q c = q d = 7 . 50 μC size 12{q rSub { size 8{c} } =q rSub { size 8{d} } = - 7 "." "50""μC"} {} . (b) Calculate the magnitude of the force on the charge q size 12{q} {} , given that the square is 10.0 cm on a side and q = 2 . 00 μC size 12{q=2 "." "00""μC"} {} .

Four point charges, one is q a, second is q b, third is q c, and fourth is q d, lie on the corners of a square. q is located at its center.

(a) Using the symmetry of the arrangement, determine the direction of the electric field at the center of the square in [link] , given that q a = q b = 1 . 00 μC size 12{q rSub { size 8{a} } =q rSub { size 8{b} } = - 1 "." "00""μC"} {} and q c = q d =+ 1 . 00 μC size 12{q rSub { size 8{c} } =q rSub { size 8{d} } "=+"1 "." "00""μC"} {} . (b) Calculate the magnitude of the electric field at the location of q size 12{q} {} , given that the square is 5.00 cm on a side.

(a)The electric field at the center of the square will be straight up, since q a size 12{q rSub { size 8{a} } } {} and q b size 12{q rSub { size 8{b} } } {} are positive and q c size 12{q rSub { size 8{c} } } {} and q d size 12{q rSub { size 8{d} } } {} are negative and all have the same magnitude.

(b) 2 . 04 × 10 7 N/C ( upward ) size 12{ {underline {2 "." "04" times "10" rSup { size 8{7} } " N/C" \( "upward" \) }} } {}

Find the electric field at the location of q a size 12{q rSub { size 8{a} } } {} in [link] given that q b = q c = q d =+ 2 . 00 nC size 12{q rSub { size 8{b} } =q rSub { size 8{c} } =q rSub { size 8{d} } "=+"2 "." "00""nC"} {} , q = 1 . 00 nC size 12{q= - 1 "." "00""nC"} {} , and the square is 20.0 cm on a side.

Find the total Coulomb force on the charge q in [link] , given that q = 1 . 00 μC size 12{q=1 "." "00""μC"} {} , q a = 2 . 00 μC size 12{q rSub { size 8{a} } =2 "." "00""μC"} {} , q b = 3 . 00 μC size 12{q rSub { size 8{b} } = - 3 "." "00""μC"} {} , q c = 4 . 00 μC size 12{q rSub { size 8{c} } = - 4 "." "00""μC"} {} , and q d =+ 1 . 00 μC size 12{q rSub { size 8{d} } "=+"1 "." "00""μC"} {} . The square is 50.0 cm on a side.

0 . 102 N , size 12{0 "." "102"" N",} {} in the y size 12{ - y ital } {} {} {} {} direction

(a) Find the electric field at the location of q a in [link] , given that q b = +10.00 μ C and q c = –5.00 μ C . (b) What is the force on q a , given that q a = +1.50 nC ?

Three point charges located at the corners of an equilateral triangle.
Point charges located at the corners of an equilateral triangle 25.0 cm on a side.

(a) Find the electric field at the center of the triangular configuration of charges in [link] , given that q a =+ 2 . 50 nC size 12{q rSub { size 8{a} } "=+"2 "." "50""nC"} {} , q b = 8 . 00 nC size 12{q rSub { size 8{b} } = - 8 "." "00""nC"} {} , and q c =+ 1 . 50 nC size 12{q rSub { size 8{c} } "=+"1 "." "50""nC"} {} . (b) Is there any combination of charges, other than q a = q b = q c size 12{q rSub { size 8{a} } =q rSub { size 8{b} } =q rSub { size 8{c} } } {} , that will produce a zero strength electric field at the center of the triangular configuration?

(a) E = 4.36 × 10 3 N/C , 35.0º , below the horizontal.

(b) No

Questions & Answers

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
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
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
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
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?
s. Reply
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 ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
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
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, General physics ii phy2202ca. OpenStax CNX. Jul 05, 2013 Download for free at http://legacy.cnx.org/content/col11538/1.2
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