Parallel conductors????? (1 Viewer)

[scrubs.]

This question is about two parallel current-carrying conductors and comes from the physics in context textbook so if anyone could explain it to me that would be great!

"Two straight parallel conducting wires carry currents of 1A and 2A respectively in opposite directions and cross a metre rule at the 50cm and 80 cm marks (ie, they lie 30cm apart) At which point on the rule is the net magnetic field zero???????'

the answer is at the 20 cm mark...so how do we go about getting this answer cos i'm confused...

 

[Bank$]

I use a ratio method which seems to work:

The ratio of the current is 1:2 therefore the equivalence point must be 2 times further away from the 2A as it is from the 1A thus 20cm mark because its 30cm from 1A and 60cm i.e. twice the distance from 2A.

Although i havnt tried i assume u can use 2 equations and equate them, Its just these questions don’t seem to come up that often

 

[xiao1985]

Strange question.

It's true that all fields (including magnetic field) fades as a funciton of inverse of distance. But I didn't expect high school to know such facts.

 

[alcalder]

OR YOU COULD Use the equation:
B = kI/r

For wire 1:
B₁ = kI₁/x

For wire 2:
B₂ = kI₂/(0.3-x)

I₁ = 1A
I₂ = 2A

The currents are in opposite directions, so the magnetic fields between the wires are in opposite directions. Thus you need to find when:

B₁ = B₂
kI₁/x = kI₂/(0.3-x)
1/x = 2/(0.3-x)

0.3-x = 2x
3x = 0.3
x = 0.1

Thus the magnetic fields cancel out 10cm away from wire 1 which is at 60cm on the ruler (but the ratios works much nicer)

 

[Bank$]

hey alcalder, xiao1985 or any of u really smart uni ppl lol does my method work by luck ? or is it proper ? cause i just found that it worked and kept using it

 

[alcalder]

Of course it works. Look at the equations again:

B= kI/r

if you equate the two equations for the two wires you can see that for B to remain the same at a point in space the current and hence the distance apart are in the same ratio.

kI₁/r₁ = kI₂/r₂

I₁ and I₂ are proportional and so are
r₁ and r₂

 

[xiao1985]

Ah dear alcalder,

I don't think the lovely cute HSC'ers are taught that formula? Hence the comment, strange =/

 

[alcalder]

Granted, that equation is not on the formula sheet BUT these are:

F=BIlsinθ --- 1

F/l = kI₁I₂/r --- 2

Take equation 1 and rewrite (and assume it is, say wire 2):

F/l = BI₂sinθ --- 3

Equate 3 and 2 and we are only interested in the 90deg angle bit because the current and magnetic field are perpendicular (because the wires are parallel)

BI₂sin90 = kI₁I₂/r

Thus

B = kI₁/r

When they simplified the Physics course they took out TOO MUCH mathematics. A lot of Physics concepts can be explained using equations (and, just quietly, this is what Uni and beyond Physics is about, maths).


Can I suggest people learn this fundamental equation that is actually used to dirive the F/l equation for two current carrying wires. If your teachers did not do that, then shame on them.

REMEMBER, you can learn as many useful equations as you want. Don't just rely on those on the formula sheet. That sheet is a luxury, not the be all and end all.

 

[xiao1985]

*bows to alcaldar

I had always been just rote learning that equation, even until now...

 

[dwatt]

How likely is this kind of question to appear in the HSC? I don't remember being taught about the field's cancelling out for parallel conductors (could reflect on my teacher though). I hope it is not an important facet of M and G!

 

[alcalder]

You were likely not taught the ins and outs of this equation, nor this equation at all, because the Physics course has been "simplified". However, I still believe that a physics students needs to understand where equations they use come from.

A lot of teachers teach the syllabus and nothing either side because they teach students to pass an exam. What ever happened to learning about physics and what it means and how it relates to what is around us? In fact, what happened to learning for the love of learning? Damn that HSC.

 

[twilight1412]

You were likely not taught the ins and outs of this equation, nor this equation at all, because the Physics course has been "simplified". However, I still believe that a physics students needs to understand where equations they use come from.

A lot of teachers teach the syllabus and nothing either side because they teach students to pass an exam. What ever happened to learning about physics and what it means and how it relates to what is around us? In fact, what happened to learning for the love of learning? Damn that HSC.

lol simplified? your being nice alcalder =)
it has pretty much been dumbed down to pub science
not there but its close =)

yes deriving equations the only one i ever remember deriving was the potential energy one =)
W = Fs
and you intergrate =)

also dwatt this was year 11 work i think or it was just ages ago
because the currents are going different ways then the magnetic fields generated will have opposing poles and at any given point the will add together to give a resultant magnetic flux density =)

ie you grab 10 magnets and it should theoretically be 10 times stronger =)
but 2 equal strength magnets a certain distance apart and in the middle there will be zero magnetic flux

and duckie @_@
refering to your first post ... we actually are supposed to know that =S
its in the syllabus and if you look at the formulas given by alclader it becomes plain =)