Two poles of the same strength attract each other with a force of magnitude F when placed at two corners of an equilateral triangle. If a north pole of the same strength is placed at the third vertex, it experiences a force of magnitude

. Let a north pole be placed at B and a south pole at C so that they attract with a force ‘F’.  A north pole placed at the third vertex A. is repelled with a force $F_1$ by the north pole at B and attracted with a force $F_2$ towards the south pole at C. Since all pole strengths are equal, $F_1=F_2=F$. The resultant force experienced by the north pole at A is given by 

$F_r^2=F_1^2+F_2^2+2F_1{F}_2\cos \left(120°\right)$

$=F^2+F^2+2F^2\times \left(-\frac{1}{2}\right)=F^2$

or $F_r=F.$