Question

The magnetic moment of a short magnet is $ 8\text{ }A{{m}^{2}}. $ The magnetic induction at appoint 20 cm away from its mid-point on (i) a axial point (ii) equatorial point respectively, will be :

• A. $ 2\times {{10}^{-4}}T\,and{{10}^{-4}}T $
• B. $ 3\times {{10}^{-4}}T\,and2\times {{10}^{-4}}T $
• C. $ 4\times {{10}^{-4}}T\,and3\times {{10}^{-4}}T $
• D. none of these

Answer 1

Answer: (A)

Magnetic induction in axial position. $ {{B}_{1}}=\frac{{{\mu }_{0}}}{4\pi }\frac{2M}{{{d}^{3}}} $ $ ={{10}^{-7}}\times \frac{2\times 8}{{{(20\times {{10}^{-2}})}^{2}}} $ $ =\frac{{{10}^{-7}}\times 16}{8\times {{10}^{-3}}}=2\times {{10}^{-4}}T $ At equatorial position $ {{B}_{2}}=\frac{{{B}_{1}}}{2} $ $ =\frac{2\times {{10}^{-4}}}{2}={{10}^{-4}}T $