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A magnetic needle with dipole moment M, is attached to a wooden bar of length $L$ (see the below figure) and placed in a uniform magnetic field of intensity $B$ . The bar and needle can revolve around point $O$ . Find the magnitude of the moment of force that will cause the rotation of the bar around point $O$ if the bar makes an angle $α$ with the direction of the lines of force of the magnetic field.

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MB sin $α$

MB sin 2 $α$

$M B (\sin α + \cos α)$

2MB tan $α$

answer is A.

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Detailed Solution

The moment of forces about $O$ , acting upon each pole of the needle will be equal to $m B (l + L) \sin α$ and $- m B L \sin α$ .

Hence, the net moment of the force acting on the bar is

$ζ = m B (l + L) \sin α - m B L \sin α$

$= m B l \sin α = (m l) B \sin α$

$= M B \sin α$

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