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Since μ 0 size 12{μ rSub { size 8{0} } } {} is exactly × 10 7 T m/A by definition, and because 1 T = 1 N/ A m size 12{1" T"=" 1N/" left (A cdot m right )} {} , the force per meter is exactly 2 × 10 7 N/m size 12{2 times "10" rSup { size 8{ - 7} } `"N/m"} {} . This is the basis of the operational definition of the ampere.

The ampere

The official definition of the ampere is:

One ampere of current through each of two parallel conductors of infinite length, separated by one meter in empty space free of other magnetic fields, causes a force of exactly 2 × 10 7 N/m size 12{2 times "10" rSup { size 8{ - 7} } " N/m"} {} on each conductor.

Infinite-length straight wires are impractical and so, in practice, a current balance is constructed with coils of wire separated by a few centimeters. Force is measured to determine current. This also provides us with a method for measuring the coulomb. We measure the charge that flows for a current of one ampere in one second. That is, 1 C = 1 A s size 12{1`C=1`A cdot s} {} . For both the ampere and the coulomb, the method of measuring force between conductors is the most accurate in practice.

Section summary

  • The force between two parallel currents I 1 size 12{I rSub { size 8{1} } } {} and I 2 size 12{I rSub { size 8{2} } } {} , separated by a distance r size 12{r} {} , has a magnitude per unit length given by
    F l = μ 0 I 1 I 2 2 πr . size 12{ { {F} over {l} } = { {μ rSub { size 8{0} } I rSub { size 8{1} } I rSub { size 8{2} } } over {2πr} } } {}
  • The force is attractive if the currents are in the same direction, repulsive if they are in opposite directions.

Conceptual questions

Is the force attractive or repulsive between the hot and neutral lines hung from power poles? Why?

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If you have three parallel wires in the same plane, as in [link] , with currents in the outer two running in opposite directions, is it possible for the middle wire to be repelled by both? Attracted by both? Explain.

Diagram showing three wires parallel to each other and in the same plane. The currents in wire 1 on the left side of the diagram and wire 3 on the right side of the diagram run opposite each other: I 1 runs form the top right to the lower left; I 3 runs from the lower left to the top right. Wire 2 is between the two, slightly closer to wire 3 than to wire 1.
Three parallel coplanar wires with currents in the outer two in opposite directions.
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Suppose two long straight wires run perpendicular to one another without touching. Does one exert a net force on the other? If so, what is its direction? Does one exert a net torque on the other? If so, what is its direction? Justify your responses by using the right hand rules.

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Use the right hand rules to show that the force between the two loops in [link] is attractive if the currents are in the same direction and repulsive if they are in opposite directions. Is this consistent with like poles of the loops repelling and unlike poles of the loops attracting? Draw sketches to justify your answers.

Diagram showing two current-carrying loops. The planes of the loops are parallel and horizontal, one above the other. In both loops, the current runs counterclockwise.
Two loops of wire carrying currents can exert forces and torques on one another.
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If one of the loops in [link] is tilted slightly relative to the other and their currents are in the same direction, what are the directions of the torques they exert on each other? Does this imply that the poles of the bar magnet-like fields they create will line up with each other if the loops are allowed to rotate?

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Electric field lines can be shielded by the Faraday cage effect. Can we have magnetic shielding? Can we have gravitational shielding?

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Problems&Exercises

(a) The hot and neutral wires supplying DC power to a light-rail commuter train carry 800 A and are separated by 75.0 cm. What is the magnitude and direction of the force between 50.0 m of these wires? (b) Discuss the practical consequences of this force, if any.

(a) 8.53 N, repulsive

(b) This forceis repulsiveand thereforethere isnever arisk thatthe twowires willtouch andshort circuit.

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The force per meter between the two wires of a jumper cable being used to start a stalled car is 0.225 N/m. (a) What is the current in the wires, given they are separated by 2.00 cm? (b) Is the force attractive or repulsive?

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A 2.50-m segment of wire supplying current to the motor of a submerged submarine carries 1000 A and feels a 4.00-N repulsive force from a parallel wire 5.00 cm away. What is the direction and magnitude of the current in the other wire?

400 A in the opposite direction

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The wire carrying 400 A to the motor of a commuter train feels an attractive force of 4 . 00 × 10 3 N/m size 12{4 "." "00" times "10" rSup { size 8{ - 3} } `"N/m"} {} due to a parallel wire carrying 5.00 A to a headlight. (a) How far apart are the wires? (b) Are the currents in the same direction?

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An AC appliance cord has its hot and neutral wires separated by 3.00 mm and carries a 5.00-A current. (a) What is the average force per meter between the wires in the cord? (b) What is the maximum force per meter between the wires? (c) Are the forces attractive or repulsive? (d) Do appliance cords need any special design features to compensate for these forces?

(a) 1 . 67 × 10 3 N/m size 12{1 "." "67" times "10" rSup { size 8{ - 3} } `"N/m"} {}

(b) 3 . 33 × 10 3 N/m size 12{3 "." "33" times "10" rSup { size 8{ - 3} } " N/m"} {}

(c) Repulsive

(d) No, these are very small forces

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[link] shows a long straight wire near a rectangular current loop. What is the direction and magnitude of the total force on the loop?

Diagram showing two current-carrying wires. Wire 1 is at the top and runs left to right with the current I 1 of fifteen amps also running left to right. Wire 2 makes a square circuit ten point zero centimeters in the vertical dimension and thirty point zero centimeters in the horizontal dimension. The top side of Wire 2 is seven point five zero centimeters below wire 1. The current in wire 2 is thirty point zero amps and runs counterclockwise: left to right along the bottom, up the right side, right to left along the top, and down the left side.
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Find the direction and magnitude of the force that each wire experiences in [link] (a) by, using vector addition.

Figure a shows the cross sections of three wires that are parallel to each other and arranged in an equilateral triangle. The bottom left wire has current of ten point zero amps into the page. The bottom right wire has a current of twenty point zero amps also into the page. The wire at the top of the triangle has current five point zero amps out of the page. The triangle that the wires make with each other is ten point zero centimeters on each side. Figure b shows four parallel wires arranged in a square that is twenty point zero centimeters on a side. The top two wires have current of ten point zero amps out of the page. The bottom two wires have current of five point zero amps into the page.

(a) Top wire: 2 . 65 × 10 4 N/m s, 10 . size 12{"10" "." 9°} {} to left of up

(b) Lower left wire: 3 . 61 × 10 4 N/m size 12{3 "." "61" times "10" rSup { size 8{ - 4} } `"N/m"} {} , 13 . size 12{"13" "." 9°} {} down from right

(c) Lower right wire: 3 . 46 × 10 4 N/m size 12{3 "." "46" times "10" rSup { size 8{ - 4} } `"N/m"} {} , 30 . size 12{"30" "." 0°} {} down from left

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Find the direction and magnitude of the force that each wire experiences in [link] (b), using vector addition.

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Questions & Answers

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
Two speakers are arranged so that sound waves with the same frequency are produced and radiated through a room. An interference pattern is created. Calculate the distance between the two speakers?
Hayne Reply
How can we calculate without any information?
Amir
I think the formulae used for this question is lambda=(ax)/D
Amir

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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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