Magnetic Field square wire loop

[faen]

Homework Statement

A current I is flowing in a square wire loop of side a. Find the approximate value of the magnetic field intensity magnitude at the point P, which is near to one of the corners in the plane of the square at the same d distance from the near two sides! (d<<a).

Homework Equations

I would guess biot and savarts law or formula of magnetic field on a straight current carrying conductor.

The Attempt at a Solution

I thought like this: B=2*I*u0/(2*pi*d)=2I*u0/(pi*d). That would be twice the magnetic field of an infinite long current conducting wire. But that was wrong and I don't know why.. Any help would be greatly appretiated.

 

[tiny-tim]

hi faen!

(try using the X₂ button just above the Reply box )

I thought like this: B=2*I*u0/(2*pi*d)=2I*u0/(pi*d). That would be twice the magnetic field of an infinite long current conducting wire.

ok, following that line of thought …

add an identical square loop, sharing that corner with the first loop

that's (effectively) two infinite straight wires, and so your formula would give the correct result for it

you now propose to divide by 2, but do you really think that the new square has as great a field at the given point as the old square? ​

start again, using the formula for a finite straight wire

(find that formula from the biot-savart law if you don't already know it)