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The combination of two bar magnets makes...

The 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.

Text Solution

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`f= (1)/( 2pi )sqrt((MB_(H))/(l ))`
` implies f _(1 ) =(1)/(2pi) sqrt (((M _(1) + M_(2) ) B _(H))/(l _(1) + l _(2))`
and `f _(2) = (1)/(2pi ) sqrt(((M _(1) - M_(2) ) B _(H))/(l _(1) + l_(2))), `where `M _(1) gt M _(2)`
or, `(f _(1) ^(2))/( f_(2)^(2))= (M_(1) + M_(2))/(M _(1) - M_(2))`
or, `(f _(1) ^(2) + f _(2) ^(2))/(f _(1)^(2) - f _(2) ^(2))= ((M _(1) + M _(2)) + (M _(1) - M_(2)))/((M _(1) + M_(2)) - (M _(1) - M_(2)))= (M _(1))/(M _(2))`
or, `(M_(1))/(M_(2)) = (100 + 4 )/(100 -4) = (13)/(12)`
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