Q. The resultant magnetic moment for the following arrangement is
(a) M
(b) 2M
(c) 3M
(d) 4M
Ans: (b)
Sol: M1 = 2 M ; M2 = 2 M ; θ = 120°
Resultant Magnetic moment
$ \displaystyle M_R = \sqrt{M_1^2 + M_2^2 + 2 M_1 M_2 cos\theta}$
$ \displaystyle M_R = \sqrt{(2M)^2 + (2M)^2 + 2 \times 2M \times 2M \times cos120}$
$ \displaystyle M_R = \sqrt{4M^2 + 4M^2 + 2 \times 2M \times 2M \times (-\frac{1}{2})}$
$ \displaystyle M_R = \sqrt{4 M^2} $
MR = 2 M