Question

The magnetic field along axis at a point at a distance d of a short, bar magnet will be

• 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}}} $

Answer 1

Answer: (C)

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}}} $