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Two magnets N1S1 and N2S2 having their m...

Two magnets `N_1S_1` and `N_2S_2` having their magnetic moments as M and 3M respectively are joined at an angle of `60^@` as shown in figure. The combination is placed on a floating cork in water. Determine the angle `theta` which the weaker magnet makes with the magnetic meridian.

Text Solution

Verified by Experts

As is clear from figure, in equilibrium,
`tau_1=tau_2`
`Mhsintheta=3MHsin (60^@-theta)`
`sin theta=3sin 60^@cos theta-3cos 60^@sin theta`
`sin theta(1+3cos 60^@)=3sin 60^@costheta`
`sin theta(1+3xx1/2)=3*sqrt3/2costheta`
`sin theta(5/2)=(3sqrt3)/(2)costheta`
`(sin theta)/(cos theta)=(3sqrt3xx2)/(2xx5)=(3xx1.732)/(5)=1.0392`, `tan theta=1*0392`, `theta=46*1^@`
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