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NEET Sample Paper NEET Sample Test Paper-73

  • question_answer
    A circular coil of radius R carries an electric current. The magnetic field due to the coil at a point on the axis of the coil located at a distance r from the centre of the coil, such that \[\operatorname{r} >> R\], varies as

    A) \[1/r\]                           

    B) \[1/{{r}^{3}}{{^{/}}^{2}}\]

    C) \[1/{{r}^{2}}\]                        

    D) \[1/{{r}^{3}}\]

    Correct Answer: D

    Solution :

    We have \[B=\frac{{{\mu }_{0}}}{4\pi }\frac{2\pi i{{R}^{2}}}{{{({{R}^{2}}+{{r}^{2}})}^{3/2}}}\] Given\[r>>R\], then we have, neglecting R, \[B=\frac{{{\mu }_{0}}}{4\pi }\frac{2\pi i{{R}^{2}}}{{{r}^{3}}}\] \[Also \,area = \pi {{R}^{2}}\] \[\therefore \,\,\,\,\,\,\,B=\frac{{{\mu }_{0}}}{2\pi }\,\frac{Ai}{{{r}^{3}}}\] \[\Rightarrow \,\,\,\,\,\,\,B\propto \frac{1}{{{r}^{3}}}\]


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