Answer:
F3 = 1.03 * 10⁻³ N : net force F3 acting on particle 3 due to the presence of the other two particles.
θ= -79.1° : direction of the net force F3
θ= 79.1° measured from the positive x axis ,clockwise
Explanation:
Theory of electrical forces
Because the particle q₃ is close to two other electrically charged particles, it will experience two electrical forces.
Equivalences
1nC= 10⁻⁹ C
Known data
k = 8.99*10⁹ N*m²/C²
q₁ = -8.7 nC = -8.7 * 10⁻⁹ C
q₂=-17.4 nC =-17.4 * 10⁻⁹ C
q₃= +8 nC= +8 * 10⁻⁹ C
d₁₃= 0.04 m
d₂₃= 0.04 m
d₁₃: distance from q₁ to q3
d₂₃: distance from q₂ to q3
Graphic attached
The directions of the individual forces exerted by q₁ and q₂ on q₃ are shown in the attached figure:
The force F₁₃ of q₁ on q₃ is attractive because the charges have opposite signs.
The force F₂₃ of q₂ on q₃ is attractive because the charges have opposite signs.
Calculation of the net force exerted for q₁ and q₂ on the charge q₃
The net force exerted for q₁ and q₂ on the charge q₃ is the algebraic sum of the forces in x-y of F₁₃ and F₂₃
Fn₃x =F₁₃x+ F₂₃x
Fn₃y = F₁₃y+F₂₃y
Calculation of the magnitudes of F₁₃ and F₂₃
To calculate the magnitudes of the forces exerted by the charges q₁, and q₂ on q₃ we apply Coulomb's law:
F₁₃=(k*q₁*q₃)/d₁₃²
F₁₃=(8.99*10⁹*8.7*10⁻⁹*8*10⁻⁹)/(0.04)² = 3.91*10⁻⁴ N
F₂₃=(k*q₂*q₃)/d₂₃²
F₂₃=(8.99*10⁹*17.4*10⁻⁹*8*10⁻⁹)/(0.04)² = 7.82*10⁻⁴ N
Calculation of the x-y components of F₁₃ and F₂₃
F₁₃x=F₁₃*cos60°= 3.91*10⁻⁴ N *cos60°= 1.955*10⁻⁴ N
F₁₃y=F₁₃*sin60°= 3.91*10⁻⁴ N *sin60°= 3.386*10⁻⁴ N
F₂₃x=F₂₃*cos60°= 7.82*10⁻⁴ *cos60°= 3.91*10⁻⁴ N
F₂₃y=F₂₃*sin60°= 7.82*10⁻⁴ *sin60°= 6.772*10⁻⁴ N
Calculation of the x-y components of Fn₃
Fn₃x = F₁₃x+F₂₃x= - 1.955*10⁻⁴ N + 3.91*10⁻⁴ N = 1.955*10⁻⁴ N
Fn₃y = F₁₃y+F₂₃y= - 3.386*10⁻⁴ N - 6.772*10⁻⁴ N = - 10.158 *10⁻⁴ N
Calculation of the magnitude of Fn₃
F3=Fn₃= 1.034 * 10⁻³ N : net force F3 acting on particle 3 due to the presence of the other two particles.
Calculation of the direction (θ) of Fn₃
θ= tan⁻¹ (Fn₃y/Fn₃x)
θ= tan⁻¹ (- 10.158 *10⁻⁴ / 1.955*10⁻⁴ N)
θ= -79.1°
θ= 79.1° measured from the positive x axis, clockwise