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 follow: As we know the general formula for finding 41 magnetic field due to a finite length wire \[B=\frac{{{\mu }_{0}}}{4\pi }\cdot \,\,\frac{i}{r}\,\,(sin\,{{\phi }_{1}}\,+\,sin\,{{\phi }_{2}})\] Here \[{{\phi }_{1}}=\,\,0{}^\circ ,\,\,\phi \,\,=\,\,54{}^\circ \] \[\therefore \,\,\,B=\frac{{{\mu }_{0}}}{4\pi }\cdot \frac{i}{r}\,(sin\,0{}^\circ \,+\,\sin \,45{}^\circ )\,\,=\,\frac{{{\mu }_{0}}}{4\pi }\,\cdot \,\,\frac{i}{\sqrt{2}l}\,\] \[\Rightarrow \,\,\,B=\frac{\sqrt{2}{{\mu }_{0}}i}{8\pi l}\]You need to login to perform this action.
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