A current-carrying loop consists of 3 identical

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

$\vec{B}_{n e t}=\frac{1}{4}\left(\frac{\mu_{0} I}{2 R}\right)(\hat{i}+\hat{j}+\hat{k})$

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