A) \[\frac{{{\mu }_{0}}}{3\pi }\times \frac{M}{{{d}^{3}}}\]
B) \[\frac{{{\mu }_{0}}}{\pi }\times \frac{M}{{{d}^{3}}}\]
C) \[\frac{{{\mu }_{0}}}{2\pi }\times \frac{M}{{{d}^{3}}}\]
D) \[\frac{{{\mu }_{0}}}{4\pi }\times \frac{M}{{{d}^{3}}}\]
Correct Answer: C
Solution :
The magnetic field with the effect of the bar magnet at an axial position at a distance is given by \[B=\frac{{{\mu }_{0}}}{4\pi }\times \frac{2Md}{{{({{d}^{2}}-{{l}^{2}})}^{2}}}\] For a short bar magnet\[{{l}^{2}}<\,\,<\,\,{{d}^{2}}\] Hence\[B=\frac{{{\mu }_{0}}}{4\pi }\times \frac{2M}{{{d}^{3}}}=\frac{{{\mu }_{0}}}{2\pi }\times \frac{M}{{{d}^{3}}}\]
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