A) \[\frac{{{\mu }_{0}}i}{2\sqrt{2}\pi l}\]
B) \[\frac{\sqrt{2}{{\mu }_{0}}i}{8\pi l}\]
C) \[\frac{{{\mu }_{0}}i}{4\pi l}\]
D) \[\frac{\sqrt{2}{{\mu }_{0}}i}{\pi l}\]
Correct Answer: B
Solution :
The magnetic field due to a finite length wire \[B=\frac{{{\mu }_{0}}}{4\pi }.\frac{i}{r}(sin{{\phi }_{1}}+\sin {{\phi }_{2}})\] Here, \[{{\phi }_{1}}={{0}^{o}}\] and \[{{\phi }_{2}}={{45}^{o}}\] \[\therefore \] \[B=\frac{{{\mu }_{0}}}{4\pi }\frac{i}{r}(sin{{0}^{o}}+sin{{45}^{o}})\] \[=\frac{{{\mu }_{0}}}{4\pi }\frac{i}{l}\frac{1}{\sqrt{2}}\] \[=\frac{\sqrt{2}{{\mu }_{0}}i}{8\pi l}\]You need to login to perform this action.
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