Solving a DC Current Magnetic Flux Problem

[Ellispson]

Homework Statement

A direct current i=10 A flows in a long straight round conductor.Find the magnetic flux through half of the wire's cross section per one metre of it's length.

Homework Equations

The Attempt at a Solution

I have spent quite a while thinking on this problem but I can't think of anything.I'd greatly appreciate it if someone could provide me with a hint of some sort.

 

[rude man]

Use Ampere's law! (Hint: may be a trick question).

 

[Ellispson]

Use Ampere's law! (Hint: may be a trick question).

Okay so,the cross sectional area through which flux is to be found is shaped like a cylinder cut into half through the axis.
Now,if I look at the curved area,the magnetic field lines will be in the shape of concentric circles and they will not cut this curved surface area at all(Hence,flux through that will be 0)
Now,if I look at the straight part.I can use Ampere's law to calculate field strength at any point inside the wire.Now,the problem I face here is that,when I do this,I get a result which says that the amount of field lines entering the straight part to the left of the axis is equal to the amount of field lines leaving.This effectively gives me the flux as 0.
Could you please tell me where my error lies?

 

[jackMybrain@ru]

Use Ampere's law! (Hint: may be a trick question).

I also thought about ampere's law: Current Intensity(J)=I/A. But how would he find the magnetic flux without the charge enclosed in A.

 

[rude man]

The wording is somewhat nebulous. I read it that the area to be considered is a radius times 1 meter length of the wire.

(At first I thought they meant the flux thru half the circular cross-section, which is what's usually meant by a wire's cross-section. That would of couse be zero.)

But if you take the area described above it has area = radius times 1 meter. That area does have a net flux thru it. You need to use Ampere's law, assume the current is uniformly distributed within the circular cross-section, then do an integration

I also thought about ampere's law: Current Intensity(J)=I/A. But how would he find the magnetic flux without the charge enclosed in A.

The charge is not the issue. The issue is current which sets up the mag. field within the wire.
.

 

[Ellispson]

The wording is somewhat nebulous. I read it that the area to be considered is a radius times 1 meter length of the wire.

(At first I thought they meant the flux thru half the circular cross-section, which is what's usually meant by a wire's cross-section. That would of couse be zero.)

But if you take the area described above it has area = radius times 1 meter. That area does have a net flux thru it. You need to use Ampere's law, assume the current is uniformly distributed within the circular cross-section, then do an integration

The charge is not the issue. The issue is current which sets up the mag. field within the wire.
.

Radius times one metre?I don't think I understand.How would that be half of the cross section?

 

[rude man]

Radius times one metre?I don't think I understand.How would that be half of the cross section?

Well, it's weird to be sure. But if you look at the wire end-on (at the circular cross-section) then the radius is one-half the diameter and so might be what they had in mind.

If you pick the whole diameter the answer would be zero since the flux would go in one radius and out the opposite radius.

 

[Ellispson]

Well, it's weird to be sure. But if you look at the wire end-on (at the circular cross-section) then the radius is one-half the diameter and so might be what they had in mind.

If you pick the whole diameter the answer would be zero since the flux would go in one radius and out the opposite radius.

Oh oh oh I get it now.Thanks a lot..