<< Chapter < Page Chapter >> Page >

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?

Got questions? Get instant answers now!

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.
Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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.
Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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.

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

[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.
Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

Questions & Answers

Calculate the work done by an 85.0-kg man who pushes a crate 4.00 m up along a ramp that makes an angle of 20.0º20.0º with the horizontal. (See [link] .) He exerts a force of 500 N on the crate parallel to the ramp and moves at a constant speed. Be certain to include the work he does on the crate an
Collins Reply
What is thermal heat all about
Abel Reply
why uniform circular motion is called a periodic motion?.
Boniface Reply
when a train start from A & it returns at same station A . what is its acceleration?
Mwdan Reply
what is distance of A to B of the stations and what is the time taken to reach B from A
BELLO
the information provided is not enough
aliyu
Hmmmm maybe the question is logical
yusuf
where are the parameters for calculation
HENRY
there is enough information to calculate an AVERAGE acceleration
Kwok
mistake, there is enough information to calculate an average velocity
Kwok
~\
Abel
what is the unit of momentum
Abel
wha are the types of radioactivity ?
Worku Reply
what are the types of radioactivity
Worku
what is static friction
Golu Reply
It is the opposite of kinetic friction
Mark
static fiction is friction between two surfaces in contact an none of sliding over on another, while Kinetic friction is friction between sliding surfaces in contact.
MINDERIUM
I don't get it,if it's static then there will be no friction.
author
It means that static friction is that friction that most be overcome before a body can move
kingsley
static friction is a force that keeps an object from moving, and it's the opposite of kinetic friction.
author
It is a force a body must overcome in order for the body to move.
Eboh
If a particle accelerator explodes what happens
Eboh
why we see the edge effect in case of the field lines of capacitor?
Arnab
what is wave
Muhammed Reply
what is force
Muhammed
force is something which is responsible for the object to change its position
MINDERIUM
more technically it is the product of mass of an object and Acceleration produced in it
MINDERIUM
wave is disturbance in any medium
iqra
energy is distributed in any medium through particles of medium.
iqra
If a particle accelerator explodes what happens
Eboh Reply
we have to first figure out .... wats a particle accelerator first
Teh
What is surface tension
Subi Reply
The resistive force of surface.
iqra
Who can tutor me on simple harmonic motion
yusuf Reply
on both a string and peldulum?
Anya
spring*
Anya
Yea
yusuf
Do you have a chit-chat contact
yusuf
I dont have social media but i do have an email?
Anya
Which is
yusuf
Where are you chatting from
yusuf
I don't understand the basics of this group
Jimmy
teach him SHM init
Anya
Simple harmonic motion
yusuf
how.an.equipotential.line is two dimension and equipotential surface is three dimension ?
syed Reply
definition of mass of conversion
umezurike Reply
Force equals mass time acceleration. Weight is a force and it can replace force in the equation. The acceleration would be gravity, which is an acceleration. To change from weight to mass divide by gravity (9.8 m/s^2).
Marisa
how many subject is in physics
Adeshina Reply
the write question should be " How many Topics are in O- Level Physics, or other branches of physics.
effiom
how many topic are in physics
Praise
Praise what level are you
yusuf
If u are doing a levels in your first year you do AS topics therefore you do 5 big topic i.e particles radiation, waves and optics, mechanics,materials, electricity. After that you do A level topics like Specific Harmonic motion circular motion astrophysics depends really
Anya
Yeah basics of physics prin8
yusuf
Heat nd Co for a level
yusuf
yh I need someone to explain something im tryna solve . I'll send the question if u down for it
Tamdy Reply
a ripple tank experiment a vibrating plane is used to generate wrinkles in the water .if the distance between two successive point is 3.5cm and the wave travel a distance of 31.5cm find the frequency of the vibration
Tamdy
hallow
Boniface
please send the answer
Boniface
the range of objects and phenomena studied in physics is
Bethel Reply
I don't know please give the answer
Boniface

Get the best College physics course in your pocket!





Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask