# Forces acting on two parallel wires carrying current which producing B

1. Dec 6, 2013

### kira506

I want to know how to calculate the force , I know the formula and such but its just that I'm not sure about the Length part , I mean if Wire1 is longer than Wire2 ,then should I take the common length between them , or just substitue with the total length ? , should F1on2=B2I(delta)l or B2I1L1

2. Dec 7, 2013

### tiny-tim

hi kira506!
the formula you're using is a simplified version of the biot-savart law, for two parallel infinite straight wires

it also works pretty accurately for two equal parallel finite straight wires, provided their lengths are substantially longer than the gap between them

this is because it assumes that the magnetic field is constant (at any particular radius) all the way along the wire … that obviously isn't true once you get beyond the end of the shorter wire!

so you need to go back to the biot-savart law itself

google "biot-savart finite straight wire", or just watch

Last edited by a moderator: Sep 25, 2014
3. Dec 8, 2013

### kira506

I'm greatly ashamed of myself , I can't seem to understand it yet , I sincerely apologize for putting you through this but I really need to understand it , all the sites write the biot savart law vectorialy and our curriculum doesn't provide us except with simplified forms for all the laws of physics ,these thing are studied in detail in college here , so I don't understand how we can imagine an infinite straight wire forming a magnetic field and even if we assumed that , how does the magnetic feild of a finite wire differ from it ,that's what hinders me in understanding the Biot Savart law

4. Dec 8, 2013

I'm guessing they want you to calculate the force per unit length. Use the Biot and Savart equation combined with Bil. To get the force per unit length you divide by l, it cancels and you don't need to know its value.

5. Dec 8, 2013

### tiny-tim

hi kira506!
the biot savart law includes a cross product

are you not familiar with cross products?

the magnetic field lines for a straight current-carrying wire will always be circles round the wire, whether it's finite or infinite (this is obvious, from symmetry)

but the circles will all be the same size for an infinite wire

in other words, the magnetic field strength will be a function B(r) that only depends on the distance r from the wire

however, for a finite wire, B will be a function of z as well (the distance along the wire): B(r,z)

when it's just B(r), you can easily tell what the function B is

when it's B(r,z), you can't, and you need to use the biot-savart law to calculate it in detail

have you watched the video i referred to?

is there any part of it you don't understand?​

6. Jan 2, 2014

### kira506

XD a point , but how will L be cancelled if each wire has a different length

7. Jan 2, 2014

### kira506

cross products .... Well Iactually don't know them (its a complicated system here,my curriculum is part of the old educational system ) Is it the product of multiplying two vectors so the resultant will be in a direcrion perpendicular to both ?
I watched the video and I couldn't understand most of it because I didn't know the difference between an infinite st.wire and a finite one ,but I'll rewatch it since you've explaineed it to me ,though I still don't get the distance part, you mean the distance from the wire or the distance of it ?, thanks a lot for being patient with me XD I know how hard it is to explain physics to someone who baely has any idea or trace of what you're syaing , sorry for the trouble and thanks a lot again

8. Jan 2, 2014

A problem here is that you haven't given us the full question. How the question is worded is relevant to the answer. I guessed that the question is at an A.S/A level standard (followed by 16 to 18 year olds In UK schools). If the question is at this level the simplified answer I guessed at is probaly all that is needed. At this level the wires are considered to be long enough for edge effects to be negligible.
If edge effects are not negligible you have to take carry out a more detailed analysis as outlined by tiny-tim.

(If the question referred to the wires as being "long" then it is probably safe to ignore edge effects)

9. Jan 2, 2014

### tiny-tim

hello kira506! happy new year!
yes (and proportional to the sine of the angle between them, so it's a maximum when the original two are perpendicular)

magnetism is full of cross products, so if you want to calculate anything complicated, you really do need to understand them
i meant both the radial distance (r) from the line of the wire and the longitudinal distance (z) along the wire

(as in cylindrical coordinates, if you know what they are)

this calculation is so complicated that you do need to use both of them

10. Jan 3, 2014

### kira506

I'm sorry , I should've mentioned the level of the answer I desired , its just that most of the answqers I get are similar to what is in my curriculum or relatively comprehensible ,but in this case turned out o be much more simplified in our books than what I've imagined , I guess my question should be more like :"if two ideal wires carrying the same current and // to eachother produce a magnetic field, but the lenght of the first wire is less than that of the second wire , will their be a mutual force between them or will the force on 1st wire (F=L1I1B2) differ from that on the 2nd ? (its just that I ask my questions hurridly , sorry again)

11. Jan 3, 2014

### kira506

I'm sorry for not having mentionned the level of my desired explanation v.v , I should've been more specific , sorry for troubling you ,but I don't know what cylindrical coordinates are ? h of cylinder and r ? So the wire is considered as a cylinder which we consider its coordinates ? So sorry again >.<

12. Jan 3, 2014

### tiny-tim

do you know what polar coordinates (r,θ) are?

EDIT: these are (r,θ) polar coordinates:

they are two-dimensional, and they cover the (x,y) plane in the above grid instead of the usual (x,y) grid squares

cylindrical coordinates are (r,θ,z) instead of (x,y,z) … the z in both is the same … the (r,θ) is the same as in polar coordinates … they are three-dimensional, and they cover the whole of (x,y,z) space

Last edited: Jan 3, 2014
13. Jan 3, 2014

Form Newton's third law,the force on the first wire will be equal in size but opposite in direction to the force on the second wire.

14. Jan 14, 2014

### kira506

Hi , Tiny tim , so sorry for being late , I had mid-year exams ,so sorry for having you bear up with me
I know theta but what does the "r" stand for ? Theta radian ? And how do they replace the x and y co-ordinates ? So sorry again

15. Jan 14, 2014

### tiny-tim

hi kira506!

i hope you did well in your exams!
"r" stands for "radius", it's the radius or radial coordinate, equal to the distance from the origin

so those circles are all "lines" of constant r (0 ≤ r < ∞)

my diagram shows polar graph paper (see eg http://incompetech.com/graphpaper/polar/), which covers the whole plane in a grid like the usual x,y grid …

you specify the position of a point by the grid-lines it lies on (or would lie on if they were there): the line of constant θ, and the circle of constant r

16. Jan 15, 2014

### kira506

Thank you c: I hope so too cx
so the "r" is the lines of co-ordinates and theta is the angle between the line (which represents distance from object to origin) and the radius representing the y co-rdinate ? And if it is so (that the radius here is the X,y and z ) if there's a radius representing that ,does that mean that thi isn't a circle and that we're dealing with a sphere ? And why are they called polar co-ordinates ? So sorry for the torrent of questions XD

17. Jan 15, 2014

### kira506

I'm extremely sorry for not replying right away , I was just trying to grasp the meaning of Newton's third law inorder to understande it but I still don't , I kinda mix it up with the impulse and collision ! So sorry ,but can you please simplify it ?

18. Jan 15, 2014

### tiny-tim

hi kira506!
i'm not sure i understand that

the straight lines are lines of constant θ and increasing r

the circles are lines of constant r and increasing θ

there is no direct relationship between the r and θ coordinates and the x and y coordinates
no, polar coordinates, as i said, are two dimensional, they cover a plane

if you add a z coordinate (exactly the same as the usual z coordinate), you get cylindrical coordinates, which of course are three-dimensional
i don't know, probably something to do with the north pole

19. Jan 17, 2014

### kira506

nevermind that , my question was based on the fact that I thought that there was a direct relationship , sorry XD but I forgot what do they have to do with the st. Wire carrying current , so sorry >.< , so can you please explain ?