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A square coil of edge l having n turns carries a current i. It is kept on a smooth horizontal plate. A uniform magnetic field B exists in a direction parallel to an edge. The total mass of the coil is M. What should be the minimum value of B for which the coil will start tipping over.

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$\frac{mg}{nil}$

$\frac{2 mg}{nil}$

$\frac{nil}{2 mg}$

$\frac{mg}{2 nil}$

answer is C.

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Detailed Solution

M a g n e t i c d i p o l e m o m e n t o f t h e c o i l, M = n l^{2} i M a g n e t i c t o r q u e, τ_{B} = M B \sin 90^{0} = n l^{2} i B G r a v i t a t i o n a l r e s t o r i g m o m e n t, τ_{G} = m g . \frac{l}{2} T h e c o i l w i l l t i p o v e r o n e e d g e i f τ_{B} > τ_{G} \Rightarrow B > \frac{m g}{2 n l i}

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