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## Homework Statement

A square wire loop of size 2a by 2a lies in the x- y plane with its center at the origin and sides parallel to the x and y axes. A counterclockwise current I runs around the loop.

(a) Find the magnetic field on the z axis. [Answer: Bz = 2μ

_{0}Ia

^{2}/[(a

^{2}+ z

^{2})(2a

^{2}+ z

^{2})

^{0.5}]]

(b) Show that for z/a >> 1 the field becomes that of a magnetic dipole, and find the magnetic moment.

## Homework Equations

Field of a magnetic dipole:

B=(μ

_{0}/4πr

^{3})*[3(m⋅r')r'-m]

where r is the distance to the field point, m is the magnetic moment, and r' is a unit vector pointing towards the field point

## The Attempt at a Solution

I have already done part a and got the correct expression for the magnetic field. For part b, I said that since z/a >> 1 the term (a

^{2}+z

^{2}) could be approximated as z

^{2}and the term (2a

^{2}+z

^{2}) could be approximated by z

^{2}. This gives me z

^{3}in the denominator which is good since it matches the equation for the field of a magnetic dipole but I can't get the rest of the terms to match. Can someone help me? I think I've either made the wrong assumption or I'm not properly evaluating the term in the square brackets in the equation for field of a magnetic dipole.