# The resultant magnetic moment for the following arrangement is

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