Magnetic field created by a wire

[Eitan Levy]

Homework Statement

x represents the distance between the wire and P.
The wire has infinite length.
What is the magnetic field created by the wire at P?

Homework Equations

B=μ₀I/2πr

The Attempt at a Solution

I thought the the first part of the wire creates a field equals to μ₀I/2πx (directed inwards the paper/screen), and that the second part doesn't affect the magnetic field at P. However the answer is μ₀I/4πx, where is my mistake? I know it's a simple problem but we have just started studying this, thanks in advance.

 

[Doc Al]

I thought the the first part of the wire creates a field equals to μ0I/2πx (directed inwards the paper/screen),

That's the field from an infinitely long current-carrying wire. (Meaning: No end in sight.) What you need is the field from a semi-infinite wire. (There are end effects.)

 

[Eitan Levy]

That's the field from an infinitely long current-carrying wire. (Meaning: No end in sight.) What you need is the field from a semi-infinite wire. (There are end effects.)

So basically because it's a semi infinite wire I need to divide the field it creates by two?

 

[Doc Al]

So basically because it's a semi infinite wire I need to divide the field it creates by two?

Exactly. (You can appeal to symmetry. An infinitely long wire can be thought of as two semi infinite wires joined together. So each piece contributes half.)

 

[Nguyen Son]

You can find it by mathematics too, hope it can help you

 

[rude man]

I would go with Biot-Savart. I guess that's what post 5 tries to do.