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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} } } {}

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(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?

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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.

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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} {} ?

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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.

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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?

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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?

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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.
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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.
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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.
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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.
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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.
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(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

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(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.)

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(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

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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.
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(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" \( "upward" \) }} } {}

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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.

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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

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(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.
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(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

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Questions & Answers

what is the fumula for calculating specific heat capacity, fusion,fission and vaporization?
Dohn Reply
Q=cm(∆t)
Emmanuel
Q=cm∆T
Muhammad
what is difference b/w vaporization and evaporation
Muhammad
evaporation is the process of extracting moisture while vaporization is process of becoming a vapor or gas
Emmanuel
From a molecular standpoint they are both cooling processes. Also, you may want to explore states of matter😊 #myTwoCents ~Shi~
Shii
cooling is a similarlity in both process I am confused in difference
Muhammad
1- Evaporation is a process where a liquid change to gas without reaching its boiling point. 2- Vaporization is a process where a liquid change to gas after reaching its boiling point. 3- Sublimation is a process where a solid changes into vapour without passing through a liquid state
Victor
I see. Evaporation is a type of vaporization, that occurs on the surface of a liquid as it changes into the gaseous phase before reaching its boiling point. hope that aids
Shii
vaporisation is cooling process while vaporization is heating process
Emmanuel
I mean to write evaporation is an heating process while vaporization is cooling process
Emmanuel
Yea here are two applications. 1- your wet washed clothes dry under the sun, the water EVAPORATES 2- when u are cooking, it reaches a point where u need to add more water because the water you added previously is getting dried. this is VAPORIZATION. Am not sure which is a cooling or heating process
Victor
vaporization occur only when the evaporation get to level where the above cloud is been (saturated) so cooling take place and started to change to liquid (eg rain fall)
Emmanuel
They are both properties of the same process so they're both cooling
Shii
what about sublimation? cooling or heating process?
Victor
exact
Muhammad
evaporation is the increase in kinetic energy of the liquid which can be gone by adding heat
Emmanuel
so its an heating process
Emmanuel
sublimation is when a solid change to gas
Emmanuel
evaporation is very definitely a cooling process. respectfully@Emmanuel when liquid turns to gas it requires more energy from its surroundings, this energy is in the form of heat, and when heat energy leaves the evaporating liquid it leaves it cooler. Thus, cooling process.
Shii
.
Shii
evaporation is very definitely a cooling process. respectfully@Emmanuel
Shii
kk
Emmanuel
You're right @Shi. I get your point
Victor
eascape velocity on the surface of Earth is 11.2 kms-1 the escape velocity on the surface of another planet of same mass as that of Earth but of 1/4 times of radius of Earth is a5.6kms-1 b11.2 kms-1 c22.4kms-1 d5.6ms-1
Muhammad
Emm.. is that a question? or..
Victor
it is McQ
Muhammad
a)5.6km/s
Alvis
c= Q/cm◇T
A.d
it's answer is 22.4
Muhammad
units...
Shii
vital
Shii
the time period of the artificial satellite is given by ?
raza
Why is there no 2nd harmonic in the classical electron orbit?
Shree Reply
how to reform magnet after been demagneted
Inuwa Reply
A petrol engine has a output of 20 kilowatts and uses 4.5 kg of fuel for each hour of running. The energy given out when 1 kg of petrol is burnt is 4.8 × 10 to the power of 7 Joules. a) What is the energy output of the engine every hour? b) What is the energy input of the engine every hour?
Morris Reply
what is the error during taking work done of a body..
Aliyu Reply
what kind of error do you think? and work is held by which force?
Daniela
I am now in this group
smart
theory,laws,principles and what-a-view are not defined. why? you
Douglas Reply
A simple pendulum is used in a physics laboratory experiment to obtain an experimental value for the gravitational acceleration, g . A student measures the length of the pendulum to be 0.510 meters, displaces it 10 o from the equilibrium position, and releases it. Using a s
Emmanuel Reply
so what question are you passing across... sir?
Olalekan
Two masses of 2 kg and 4 kg are held with a compressed spring between them. If the masses are released, the spring will push them away from each other. If the smaller mass moves off with a velocity of 6m/s, what is the stored energy in the spring when it is compressed?
Emmanuel Reply
54 joule
babar
how?
rakesh
Reduce that two body problem into one body problem. Apply potential and k. E formula to get total energy of the system
rakesh
i dont think dere is any potential energy... by d virtue of no height present
Olalekan
there is compressed energy,dats only potential energy na?
rakesh
yes.. but... how will u approach that question without The Height in the question?
Olalekan
Can you explain how you get 54J?
Emmanuel
Because mine is 36J
Emmanuel
got 36J too
Douglas
OK the answer is 54J Babar is correct
Emmanuel
Conservation of Momentum
Emmanuel
woow i see.. can you give the formula for this
joshua
Two masses of 2 kg and 4 kg are held with a compressed spring between them. If the masses are released, the spring will push them away from each other. If the smaller mass moves off with a velocity of 6m/s, what is the stored energy in the spring when it is compressed? Asume there is no external force.
Emmanuel Reply
Please help!
Emmanuel
please help find dy/dx 2x-y/x+y
Inuwa
By using the Quotient Rule dy/dx = 3y/(x +y)²
Emmanuel
3y/(x+y)²
Emmanuel
may be by using MC^2=MC^2 and Total energy=kinetic energy +potential energy so 1st find kinetic energy and den find potential energy which is stored energy
rakesh
i think i m correct
rakesh
But how?
Emmanuel
3y/(x+y)²
Douglas
what's the big bang?
kwame Reply
yes what is it?
LamaBbake
it is the explanation of how the universe began
Zainab
yes
Ana
explain
Chinagorom
in
Chinagorom
it is a theory on how the universe began. to understand more I would suggest researching the topic online.
david
thanks guys
kwame
if a force of 12N is applied to load of 200g what us the work done
Joshua Reply
We can seek accelation first
Nancy
we are given f=12 m=200g which is 0.2kg now from 2nd law of newton a= f/m=60m/s*2 work done=force applied x displacement cos (theta) w= 12x60 =720nm/s*2
Mudang
this very interesting question very complicated for me, í need urgent help. 1,two buses A and B travel along the same road in the same direction from Harper city (asume They both started from the same point) to Monrovia. if bus A maintains a Speedy of 60km/h and bus B a Speedy of 75km/h, how many
mohammed
hours Will it take bus B to overtake bus A assuming bus B starts One hour after bus A started. what is the distance travelled by the buses when They meet?.
mohammed
pls í need help
mohammed
4000 work is done
Ana
speed=distance /time distance=speed/time
Ana
now use this formula
Ana
what's the answer then
Julius
great Mudang
Kossi
please Ana explain 4000 ?
babar
hey mudang there is a product of force and acceleration not force and displacement
babar
@Mohammed answer is 0.8hours or 48mins
Douglas
nice
A.d
its not possible
Olalekan
í want the working procedure
mohammed
the answer is given but how Will One arrive at it. the answers are 4hours and 300m.
mohammed
physics is the science that studies the non living nature
isidor Reply
ancient greek language physis = nature
isidor
what is phyacs
technical Reply
if i am going to start studying physics where should i start?
BRIAN Reply
I think from kinematics
Nancy
You can find physics books at the library or online. That's how I started.
Chelsea
And yes, kinematics is usually where you can begin.
Chelsea
study basic algebra and calculus and can start from classical mechanics
Mudang
yes think so but dimension is the best starting point
Obed
3 formula's of equations of motion
benjamin Reply
vf=vi+at........1 s=vit+1/2(at)2 vf2=vi2+2as
Ana
solve the formula's please
benjamin
those are the three .. what you wanna solve ?
Nihrantz
For first equation simply integrate formula of acceleration in the limit v and u
Tripti
For second itegrate velocity formula by ising first equation
Tripti
similarly for 3 one integrate acceleration again by multiplying and dividing term ds
Tripti
any methods can take to solve this eqtions
a=vf-vi/t vf-vi=at vf=vi+at......1
Ana
suppose a body starts with an initial velocity vi and travels with uniform acceleration a for a period of time t.the distance covered by a body in this time is "s" and its final velocity becomes vf
Ana
what is the question dear
Zeeshan
average velocity=(vi+vf)/2 distance travelled=average velocity ×time therefore s=vi+vf/2×t from the first equation of motion ,we have vf =vi+at s=[vi+(vi+at)]/2×t s=(2vi+at)/2×t s=bit+1/2at2
Ana
find the distance
Ana
how
Zeeshan
v=u+at,v^2=(u^2) +2as,s=2u +(1/2)gt^2
Emmanuel
Practice Key Terms 6

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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