Question:
A current-carrying loop consists of 3 identical quarter circles of radius R, lying in the positive quadrants of the x-y, y-z, and z-x planes with their centres at the origin, joined together. Find the direction and magnitude of B at the origin.
Solution:
The vector sum of the magnetic field at the origin due to the quarter is given as
$\vec{B}_{n e t}=\frac{1}{4}\left(\frac{\mu_{0} I}{2 R}\right)(\hat{i}+\hat{j}+\hat{k})$