• # question_answer A current carrying loop consists of three 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 magnetic field at the origin.

For the current carrying loop quarter circles of radius R, lying in the positive quadrants of the XY-plane. ${{B}_{1}}=\frac{{{\mu }_{0}}}{4\pi }\frac{I(\pi /2)}{R}\hat{k}=\frac{{{\mu }_{0}}}{4}\frac{I}{2R}\hat{k}$ For the current carrying loop quarter circles of radius R, tying in the positive quadrants of the YZ-plane magnetic field at the centre.             ${{B}_{2}}=\frac{{{\mu }_{0}}}{4}\frac{I}{2R}\hat{i}$ Similarly, for the current carrying loop quarter circles of radius R, lying in the positive quadrants of the ZX-plane             ${{B}_{3}}=\frac{{{\mu }_{0}}}{4}\frac{I}{2R}\hat{j}$ Current carrying loop consists of three identical quarter circles of radius R, lying in the positive quadrants of the X-Y, V-Z and Z-X planes with their centres at the origin, joined together is equal to the vector sum of magnetic field due to each quarter and given by             $B=\frac{1}{4\pi }(\hat{i}+\hat{j}+\hat{k})\frac{{{\mu }_{0}}I}{2R}$
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