Question

Three charges of magnitude 3.0 x10^-4 C each are located atx = 1.0 m, y = 0.0 m,at x = 0.0 m, y =0.0 m and at x =-1.0 m, y = 0.0 m. The one in themiddle is negative, while the other two are positive. What is thenet Coulombic force exerted by them on a negative 3.0x 10^-5 C charge located atx = 0.0 m, y = 2.0 m? (The value of k is 9.0 x10⁹ N*m²/C².)

a. 87 N attractive
b. 87 N repulsive
c. 120 N repulsive
d. 120 N attractive

Answer 1

The hypoteneus of the right Δ,

distance of the charge above from the end charges)is =√(1 +4) = √5 cm

The forces,

         F₁ = F₂ =9x10⁹x3x3x10^-9/5

                     = 16.2 N attraction

The force F₃ =9x10⁹x3x3x10^-9/4

                     = 20.25 N repulsion

Resolve into rectangular components along y axis and xaxis

The x components cancel out.

The resultant force, R =2.F₁ Cos θ - F₃,

where Cos θ =2/√5 = 0.8944.

Hence,

                R = 2x16.2x0.8944 - 20.25 N

                     =28.98 - 20.25

                    = 8.73 N toward the origin.

This is attractive force.

But the Choice (a) is 87 N attractive.

I think my answer is correct.