Ampere's law and magnetic strength

[lemaire]

Homework Statement

You have 16 m of 0.7 mm diameter copper wire and a battery capable of passing 21 A through the wire.
What magnetic field strength could you obtain at the center of a single circular loop made from the wire?

Homework Equations

Ampere's law

The Attempt at a Solution

I believe that the radius inside the loop will be 0.7mm and the radius of the loop will be the circumference of the wire divided by 2pie. At the right side of Ampere's law, which radius will be used?

Thanks

 

[JoAuSc]

0.7 mm is the diameter of the copper wire, not the radius of the loop.

 

[lemaire]

My question is this: we have at the left of Ampere's law B2piR. Is this R(radius) the circumference divided by 2pie?. If we set up a surface like a Gaussian surface, we have an inside radius which is half the original diameter of the wire(0.7/2).

 

[JoAuSc]

The circumference of the loop is the length of the wire used to make the loop, and you can calculate the radius of the loop from that. The radius of the wire plays no role in this problem.

Also, you would need the Biot-Savart law to calculate the current at the center of a loop. For a straight wire you have cylindrical symmetry, where the magnetic field is constant for circles about the wire, but for a wire loop that's no longer true, so you need the Biot-Savart law.