Question

Three magnets of same length but moments $M,2M$ and $3M$ are arranged in the form of an equilateral triangle with opposite poles nearer, the resultant magnetic moment of the arrangement is:

• A. $6M$
• B. $zero$
• C. $\sqrt{3}M$
• D. $\frac{\sqrt{3}}{2}M$

Answer 1

The correct option is C $\sqrt{3}M$

As clear from the picture that we have to calculate basically the resultant of three vectors representing magnetic moments by three sides of an equilateral triangle.

Resultant of M and 2M is $R=\sqrt{M^2+{4M}^2+2\ast 2M\ast M\ast Cos{120}^0}=\sqrt{3}M$

and the direction of this resultant is ${\tan }^{-1}\frac{2MSin{120}^0}{{2MCos120}^0+M}=-{90}^0$

Now the resultant of this vector and 3M is further solved and also the angle between them is ${150}^0$

$=\sqrt{9M^2+{3M}^2+2\ast \sqrt{3}M\ast 3M\ast cos{150}^0}=\sqrt{3}M$