three charges of 5micro coloumb are placed at the vertices of equilateral triangle of side 10cm the force on 1micro coulomb of charge at centre of triangle will be

Figure shows the system of charge configuration on vertex of equilateral triangle. Direction of forces also indicated in figure.

 

Since the given equilateral triangle has 10 cm side, distance between charge at centre and charge at any vertex is 5 √3 cm .

 

All forces have equal magnitude

 

| F₁ | = | F₂ | = | F₃ | = K × ( 5 × 10^-12 ) / ( 75 × 10^-4 ) = ( 9 × 10⁹ × 5 × 10^-12 ) / ( 75 × 10^-4 ) = 0.06 N

 

where K = 1/( 4πε_o ) = 9 × 10⁹ N m² C^-2 is Coulomb's constnat

 

Resultant of F₂ and F₃  is 2F cos60 N along the direction OA , where F = 0.06 N

 

Resultant of F₂ and F3 = F_R = 0.06 N

 

Since F_R and F₁ are equal in magnitude but opposite in direction, net force is zero.

 

Sum of the forces acting at charge at centre is zero.