# 13.6 Conductors and electric fields in static equilibrium  (Page 5/11)

 Page 5 / 11

(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 ${q}_{a}={q}_{d}$ and ${q}_{b}={q}_{c}$

(a) What is the direction of the total Coulomb force on $q$ in [link] if $q$ is negative, ${q}_{a}={q}_{c}$ and both are negative, and ${q}_{b}={q}_{c}$ 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 ${q}_{a}={q}_{d}$ and ${q}_{b}={q}_{c}$ . First show that $q$ 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 $q$ from the center of the square.

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

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?

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?

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.

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

What is the force on the charge located at $x=8.00 cm$ in [link] (a) given that $q=1\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{μC}$ ?

(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) ${E}_{x=\text{1.00 cm}}=-\infty$

(b) $2\text{.}\text{12}×{\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}\text{N/C}$

(c) one charge of $+q$

(a) Find the electric field at $x=5.00 cm$ in [link] (a), given that $q=1.00\phantom{\rule{0.25em}{0ex}}\text{μC}$ . (b) At what position between 3.00 and 8.00 cm is the total electric field the same as that for $–2q$ 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 $q=1.00\phantom{\rule{0.25em}{0ex}}\text{μC}$ . (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 $q$ in the figure below, given that ${q}_{a}={q}_{b}\text{=+}7\text{.}\text{50}\phantom{\rule{0.25em}{0ex}}\text{μC}$ and ${q}_{c}={q}_{d}=-7\text{.}\text{50}\phantom{\rule{0.25em}{0ex}}\text{μC}$ . (b) Calculate the magnitude of the force on the charge $q$ , given that the square is 10.0 cm on a side and $q=2\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{μC}$ .

(a) Using the symmetry of the arrangement, determine the direction of the electric field at the center of the square in [link] , given that ${q}_{a}={q}_{b}=-1\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{μC}$ and ${q}_{c}={q}_{d}\text{=+}1\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{μC}$ . (b) Calculate the magnitude of the electric field at the location of $q$ , 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 ${q}_{a}$ and ${q}_{b}$ are positive and ${q}_{c}$ and ${q}_{d}$ are negative and all have the same magnitude.

(b) $2\text{.}\text{04}×{\text{10}}^{7}\phantom{\rule{0.25em}{0ex}}\text{N/C}\phantom{\rule{0.25em}{0ex}}\left(\text{upward}\right)$

Find the electric field at the location of ${q}_{a}$ in [link] given that ${q}_{b}={q}_{c}={q}_{d}\text{=+}2\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{nC}$ , $q=-1\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{nC}$ , and the square is 20.0 cm on a side.

Find the total Coulomb force on the charge $q$ in [link] , given that $q=1\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{μC}$ , ${q}_{a}=2\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{μC}$ , ${q}_{b}=-3\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{μC}$ , ${q}_{c}=-4\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{μC}$ , and ${q}_{d}\text{=+}1\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{μC}$ . The square is 50.0 cm on a side.

$0\text{.}\text{102}\phantom{\rule{0.25em}{0ex}}\text{N},$ in the $-y$    direction

(a) Find the electric field at the location of ${q}_{a}$ in [link] , given that ${q}_{\text{b}}=+10.00\phantom{\rule{0.25em}{0ex}}\mu \text{C}$ and ${q}_{\text{c}}=–5.00\phantom{\rule{0.25em}{0ex}}\mu \text{C}$ . (b) What is the force on ${q}_{a}$ , given that ${q}_{\text{a}}=+1.50\phantom{\rule{0.25em}{0ex}}\text{nC}$ ?

(a) Find the electric field at the center of the triangular configuration of charges in [link] , given that ${q}_{a}\text{=+}2\text{.}\text{50}\phantom{\rule{0.25em}{0ex}}\text{nC}$ , ${q}_{b}=-8\text{.}\text{00}\phantom{\rule{0.25em}{0ex}}\text{nC}$ , and ${q}_{c}\text{=+}1\text{.}\text{50}\phantom{\rule{0.25em}{0ex}}\text{nC}$ . (b) Is there any combination of charges, other than ${q}_{a}={q}_{b}={q}_{c}$ , that will produce a zero strength electric field at the center of the triangular configuration?

(a) $\stackrel{\to }{E}=4.36×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{N/C},\phantom{\rule{0.25em}{0ex}}35.0º$ , below the horizontal.

(b) No

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
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?
what is a peer
What is meant by 'nano scale'?
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
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
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?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
How we can toraidal magnetic field
How we can create polaidal magnetic field
4
Because I'm writing a report and I would like to be really precise for the references
where did you find the research and the first image (ECG and Blood pressure synchronized)? Thank you!!