A) \[\frac{\sqrt{2}{{\mu }_{0}}i}{\pi l}\]
B) \[\frac{{{\mu }_{0}}i}{4\pi l}\]
C) \[\frac{\sqrt{2}{{\mu }_{0}}i}{8\pi l}\]
D) \[\frac{{{\mu }_{0}}i}{2\sqrt{2}\pi l}\]
Correct Answer: C
Solution :
The given situation can be redrawn as follows. As we know the general formula for finding 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, \[{{\phi }_{1}}={{0}^{o}},\,\,\phi ={{45}^{o}}\] \[\therefore \] \[B=\frac{{{\mu }_{0}}}{4\pi }.\frac{i}{r}\,(\sin \,{{0}^{o}}+\sin {{45}^{o}})\] \[=\frac{{{\mu }_{0}}}{4\pi }.\frac{i}{\sqrt{2}l}\] \[\Rightarrow \] \[B=\frac{\sqrt{2}{{\mu }_{0}}i}{8\pi l}\]You need to login to perform this action.
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