Ampere's Law vs Biot-Savart arouns a Square

[teroenza]

Homework Statement

A conductor in the shape of a square loop of edge length l = 0.360 m carries a current I = 10.0 A. Calculate the magnitude and direction of the magnetic field at the center of the square.

Homework Equations

∮B⃗ ⋅dr⃗ =μ0 Ienclosed Ampere's Law

B=μ04π ∫I dl⃗ ×rˆr2 Biot-Savart

The Attempt at a Solution

I have seen the solution and gotten the correct answer using the formula for the B field surrounding a long, thin, conductor, derived from the Biot-Savart law.
B=(mu_0*I)/(2*pi*a) , where a is the distance from the wire to point in question.
My question is why is not possible to use Ampere's law to solve this problem. I am still in the process of tying to learn/understand Ampere's law.

Thank you

 

[ehild]

My question is why is not possible to use Ampere's law to solve this problem. I am still in the process of tying to learn/understand Ampere's law.

How would you use Ampere's Law?

ehild

 

[teroenza]

By taking the closed line integral around the square, but that would enclose no net current. If I took the closed path for the line integral to be around the wire perpendicular to the current flow I get the same formula as that derived from Biot-Savart. However I then can't then seem to take into account the 4 lengths.

 

[ehild]

When we use Ampere's Law to calculate the magnetic field around an infinite line of current we assume that B is tangential to the integration path (a circle) and uniform in magnitude. It is not valid in this case. You do not know B, it is certainly different inside the loop and outside, so you cannot calculate the line integral.

ehild

 

[teroenza]

Thank you very much.