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  • 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

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

Option: 1

\mathrm{\sqrt{3} F }


Option: 2

\mathrm{F }


Option: 3

\mathrm{\sqrt{2} F }


Option: 4

\mathrm{2 F}


Answers (1)

best_answer

Refer to Fig. 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 \mathrm{F_1}  by the north pole at B and attracted with a force \mathrm{F_2}  towards the south pole at C. Since all pole strengths are equal, \mathrm{F_1=F_2=F} . The resultant force experienced by the north pole at A is given by

\mathrm{F_r^2 =F_1^2+F_2^2+2 F_1 F_2 \cos \left(120^{\circ}\right) \\ }

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

or \mathrm{ F_r=F } , which is choice (b)
\mathrm{\left(\because F_1=F_2=F\right) }

Posted by

Devendra Khairwa

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