Q. Three identical thin bar magnets each of moment M are placed along three adjacent sides of a regular hexagon as shown in figure. The resultant magnetic moment of the system is
(a) M
(b) M√3
(c) M√2
(d) 2M
Ans: (d)
Sol: $\displaystyle \vec{M_R} = M \hat{i} + (M cos 60 \hat{i} + M sin 60 \hat{j}) + (M cos 60 (-\hat{i}) + M sin60 \hat{j})$
$ \displaystyle \vec{M_R} = M \hat{i} + 2 M sin 60 \hat{j} $
$ \displaystyle \vec{M_R} = M \hat{i} + 2 M \times \frac{\sqrt{3}}{2} \hat{j} $
$ \displaystyle \vec{M_R} = M \hat{i} + \sqrt{3} M \hat{j} $
$\displaystyle M_R = \sqrt{M^2 + (\sqrt{3}M)^2} $
= 2 M