- #1
Potatochip911
- 318
- 3
Homework Statement
A wire is formed into the shape of a square of edge length L. Show that when the current in
the loop is I, the magnetic field at point P a distance x from the center of the square along its axis is $$B=\frac{\mu_0 IL^2}{2\pi(x^2+L^2/4)\sqrt{x^2+L^2/2}}$$
Homework Equations
##d\vec{B}=\frac{\mu_0}{4\pi}\frac{I\vec{ds}\times\hat{r}}{r^2}##
The Attempt at a Solution
##d\vec{B}=\frac{\mu_0}{4\pi}\frac{I\vec{ds}\sin\theta}{r^2}## where ##\theta## is the angle between ##\hat{r}## and ##\vec{ds}## therefore ##\sin\theta=\sqrt{\frac{x^2+L^2/4}{z^2+x^2+L^2/4}}##
From the symmetry of the problem it's clear that only the components parallel to ##x## will be leftover which seem to be given by ##\sin\phi## but in the solution they are given by ##\cos\phi## which doesn't make any sense to me.