# Three equal charges are placed at the corners of an equilateral triangle 8m on a side. What are the magnitude of the force on each charge if the charges are each 2 C? The figure is below. All three charges are equal means all forces are equal. Also because the charges have the same sign all the forces are of repelling type, which means that their direction is to the outside of the triangle.

`F_12=F_21=F_13=F_31=F_23=F_32`

`F_(nm) = F_(mn) = k_e*Q^2/R^2 =9*10^9*2^2/8^2 =5.625*10^8 N`

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The figure is below. All three charges are equal means all forces are equal. Also because the charges have the same sign all the forces are of repelling type, which means that their direction is to the outside of the triangle.

`F_12=F_21=F_13=F_31=F_23=F_32`

`F_(nm) = F_(mn) = k_e*Q^2/R^2 =9*10^9*2^2/8^2 =5.625*10^8 N`

The resultant `F` of each two by two forces can be found by adding them as vectors, head to tail.

`|F|=|F_(21) +F_(31)| = sqrt(F(21)^2+F_(31)^2- 2*F(21)*F(31)*cos(alpha)) =`

`=5.625*10^8*sqrt(1+1-cos(120))=5.625*10^8*sqrt(2.5) =8.89*10^8 N`

Answer: The resultant force on each charge is 8.89*10^8 N

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