NEET-XII-Physics
36: Permanent Magnets
- #22The combination of two bar magnets makes 10 oscillations per second in an oscillation magnetometer when like poles are tied together and 2 oscillations per second when unlike poles are tied together. Find the ratio of the magnetic moments of the magnets. Neglect any induced magnetism.Ans : Given:
Number of oscillations per second made by the combination of bar magnets with like poles, `` {\nu }_{1}``= 10 s`` -1``
Number of oscillations per second made by the combination of bar magnets with unlike poles, `` {\nu }_{2}`` = 2 s`` -1``
The frequency of oscillations in the magnetometer `` \left(\nu \right)`` is given by
`` \upsilon =\frac{1}{2\,\mathrm{\,\pi \,}}\sqrt{\frac{M{B}_{\,\mathrm{\,H\,}}}{I}}``
When like poles are tied together, the effective magnetic moment is
M = M1 - M2
When unlike poles are tied together, the effective magnetic moment is
M = M1 + `` {M}_{2}``
As the frequency of oscillations is directly proportional to the magnetic moment,
`` \frac{{\upsilon }_{1}}{{\upsilon }_{2}}=\sqrt{\frac{{M}_{1}-M{\hspace{0.17em}}_{2}}{{M}_{1}+{M}_{2}}}``
`` \Rightarrow {\left(\frac{10}{2}\right)}^{2}=\frac{{M}_{1}-{M}_{2}}{{M}_{1}+{M}_{2}}``
`` \Rightarrow \frac{25}{1}=\frac{{M}_{1}-{M}_{2}}{{M}_{1}+{M}_{2}}``
`` \Rightarrow \frac{25+1}{25-1}=\frac{{M}_{1}-{M}_{2}+{M}_{1}+{M}_{2}}{{M}_{1}-{M}_{2}-{M}_{1}-{M}_{2}}``
`` \Rightarrow \frac{26}{24}=\frac{2{M}_{1}}{-2{M}_{2}}``
`` \Rightarrow \frac{{M}_{1}}{{M}_{2}}=-\frac{26}{24}=-\frac{13}{12}``
Hence, the ratio of the effective magnetic moment is `` -\frac{13}{12}``.
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