Respuesta :
Answer:
F = k Q² / L² (4.82 i ^ - 8.82 j ^ N , F = k Q² / L² 10.05 N , θ = 298⁰
Explanation:
To find the electric force we must use Coulomb's law
F = k q₁ q₂ / r₁₂²
Where k is the Coulomb constant that is worth 8.99 10⁹ N m² / C², q is the value of the charges and r the distance between them
In our case the total force is
F = F₁₂ + F₃₂ + F₄₂
In the attached we can see the location of the charges. Distance
r₁₂ = L
r₃₂ = L
r₄₂ = √ L² + L² = L √ 2
Let us explicitly write the equation, remember that force is a vector equation,
X axis
Fₓ = F₁₂ +[tex]F_{42x}[/tex]
Y Axis
[tex]F_{y}[/tex]= - F₃₂ - [tex]F_{42y}[/tex]
With we have a square the angle of F₄₂ is 45⁰, using trigonometry we can find its components
cos 45 = [tex]F_{42x}[/tex] / F₄₂
sin 45 = [tex]F_{42y}[/tex] / F₄₂
[tex]F_{42x}[/tex] = F₄₂ cos 45
[tex]F_{42y}[/tex] = F₄₂ sin45
Let's replace
Fₓ = k Q 2Q / L² + k 4Q 2Q / 2L² cos 45
[tex]F_{y}[/tex] = - k 3Q 2Q / L² - k 4Q 2Q / 2L² sin 45
Fₓ = k Q² (2 + 4 cos 45) = k Q² 4.82
[tex]F_{y}[/tex] = - k Q² (6 + 4 sin 45) = k Q² 8.82
We can give strength in two ways
F = k Q² / L² (4.82 i ^ - 8.82 j ^ N
In the form of magnitude and angle
F = Ra Fₓ² + [tex]F_{y}[/tex] ²
F = kQ² / L² RA (4.82² + 8.82²)
F = k Q² / L² 10.05 N
θ = tan⁻¹ [tex]F_{y}[/tex] / Fₓ
θ = tan⁻¹ (-8.82 / 4.82)
θ = -61.34 = 298⁰
