# Why will current flow obliquely (Irodov Problem)?

## Main Question or Discussion Point

So i was doing a question from Irodov(Q 3.238) & got stuck for hours (as expected)

The question goes -
A thin conducting strip of width h is tightly wound in the shape of a very long coil with cross-section radius R to make a single layer straight solenoid. A direct current I flows through the strip. Find the magnetic induction inside and outside the solenoid as a function of the distance r from its axis.

After looking at the solution, it said that current will flow obliquely in the strip i.e. current density will have two perpendicular components.

I don't understand this. Why is it necessary that current will flow obliquely & not along the length?
And if this is the case, then current should flow obliquely in all 2-D objects.

Also, I would like to know how do we determine this kind of current distribution(like in 3-D & other 2-D objects).

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Do you have a sketch of the setup?

I would expect that current density is nearly constant along the strip and in strip direction, if the frequency is not too high and the magnetic field not too strong.

The question goes -
A thin conducting strip of width h is tightly wound in the shape of a very long coil with cross-section radius R to make a single layer straight solenoid. A direct current I flows through the strip. Find the magnetic induction inside and outside the solenoid as a function of the distance r from its axis.

After looking at the solution, it said that current will flow obliquely in the strip i.e. current density will have two perpendicular components.

I don't understand this. Why is it necessary that current will flow obliquely & not along the length?
Where is obliquely defined? Most likely it is in reference to the resulting solenoid axis of symmetry, not the strip itself. Current is forced to flow along the strip. You have then a helical path of current flow, with tanθ = 2πR/h, θ being the projected angle of current flow at any point on the solenoid, wrt solenoid axis. Now take advantage of the properties of the two components of current flow. One of relative magnitude sinθ is the solenoidal current that generates a purely axial, uniform, and internal-only B field. The other, of relative magnitude cosθ, is the axial flow component that yields an external-only circular B field a la Biot-Savart formula for straight wire of radius R. This assumes a very thin strip so we can ignore any B field profile through the strip thickness. My take anyway - accepting no responsibility if it's a wrong steer!
And if this is the case, then current should flow obliquely in all 2-D objects.
Also, I would like to know how do we determine this kind of current distribution(like in 3-D & other 2-D objects).
Wrong take on the situation I would suggest.

So i was doing a question from Irodov(Q 3.238) & got stuck for hours (as expected)

The question goes -
A thin conducting strip of width h is tightly wound in the shape of a very long coil with cross-section radius R to make a single layer straight solenoid. A direct current I flows through the strip. Find the magnetic induction inside and outside the solenoid as a function of the distance r from its axis.

After looking at the solution, it said that current will flow obliquely in the strip i.e. current density will have two perpendicular components.

I don't understand this. Why is it necessary that current will flow obliquely & not along the length?
And if this is the case, then current should flow obliquely in all 2-D objects.

Also, I would like to know how do we determine this kind of current distribution(like in 3-D & other 2-D objects).
I think you misunderstood them. It is oblique relative to the cylinder not to the strip's longitudinal axis.
The components of the current density are given in cylindrical coordinates, along the z direction (axis of the cylinder) and tangent to the cylinder.

Where is obliquely defined? Most likely it is in reference to the resulting solenoid axis of symmetry, not the strip itself. Current is forced to flow along the strip. You have then a helical path of current flow, with tanθ = 2πR/h, θ being the projected angle of current flow at any point on the solenoid, wrt solenoid axis. Now take advantage of the properties of the two components of current flow. One of relative magnitude sinθ is the solenoidal current that generates a purely axial, uniform, and internal-only B field. The other, of relative magnitude cosθ, is the axial flow component that yields an external-only circular B field a la Biot-Savart formula for straight wire of radius R. This assumes a very thin strip so we can ignore any B field profile through the strip thickness. My take anyway - accepting no responsibility if it's a wrong steer!
How could i miss that? Yeah you're absolutely correct, Thank you very much.
Wrong take on the situation I would suggest.
Yeah, just ignore that part.

I think you misunderstood them. It is oblique relative to the cylinder not to the strip's longitudinal axis.
The components of the current density are given in cylindrical coordinates, along the z direction (axis of the cylinder) and tangent to the cylinder.
Now, I just feel like a fool.

Thank You very much people. I appreciate you're help.