Respuesta :
Answer:
speed when it reaches y = 4.00cm is
v = 14.9 g.m/s
Explanation:
given
q₁=q₂ =2.00 ×10⁻⁶
distance along x = 3.00cm= 3×10⁻²
q₃= 4×10⁻⁶C
mass= 10×10 ⁻³g
distance along y = 4×10⁻²m
r₁ = [tex]\sqrt{3^{2} +2^{2} }[/tex] = [tex]\sqrt{13}[/tex] = 3.61cm = 0.036m
r₂ = [tex]\sqrt{4^{2} + 3^{2} }[/tex] = [tex]\sqrt{25}[/tex] = 5cm = 0.05m
electric potential V = [tex]\frac{kq}{r}[/tex]
change in potential ΔV = [tex]V_{1} - V_{2}[/tex]
ΔV = [tex]\frac{2kq_{1} }{r_{1}} - \frac{2kq_{2} }{r_{2} }[/tex] , where [tex]q_{1} = q_{2}=[/tex]2.00μC
ΔV = [tex]2kq(\frac{1}{r_{1}} - \frac{1}{r_{2} })[/tex]
ΔV = 2 × 9×10⁹ × 2×10⁻⁶ × [tex](\frac{1}{0.036} - \frac{1}{0.05} )[/tex]
ΔV= 2.789×10⁵
[tex]\frac{1}{2}mv^{2}[/tex] = ΔV × q₃
[tex]\frac{1}{2}[/tex] ˣ 10×10⁻³ ×v² = 2.789×10⁵× 4 ×10⁻⁶
v² = 223.12 g.m/s
v = 14.9 g.m/s
The speed of the charge q₃ when it starts from rest at y = 2 cm and reaches y = 4 cm is; v = 14.89 m/s
We are given;
Charge 1; q₁ = 2.00 μC = 2 × 10⁻⁶ C
Charge 2; q₂ = 2.00 μC = 2 × 10⁻⁶ C
Distance of charge 1 along x = 3 cm = 3 × 10⁻² m
Distance of charge 2 along x = -3 cm = -3 × 10⁻² m
Charge 3; q₃ = +4.00 μC = 4 × 10⁻⁶ C
mass; m = 0.01 g
distance of charge 3 along y = 4 cm = 4 × 10⁻² m
q₃ starts from rest at y = 2 × 10⁻² m and reaches y = 4 × 10⁻² m.
Thus;
Distance of charge 1 from the initial position of q₃;
r₁ = √((3 × 10⁻²)² + ((2 × 10⁻²)²)
r₁ = 0.0361 m
Distance of charge 2 from the final position of q₃;
r₂ = √((3 × 10⁻²)² + ((4 × 10⁻²)²)
r₂ = 0.05 m
Now, formula for electric potential is;
V = kq/r
Where k = 9 × 10⁹ N.m²/s²
Thus,change in potential is;
ΔV = V₁ - V₂
Now, Net V₁ = 2kq₁/r₁
Net V₂ = 2kq₂/r₂
Thus;
ΔV = 2kq₁/r₁ - 2kq₂/r₂
ΔV = (2 × 9 × 10⁹)[(2 × 10⁻⁶/0.0361) - (2 × 10⁻⁶/0.05)]
ΔV = 277229.92 V
Now, from conservation of energy;
½mv² = q₃ΔV
Thus;
½ × 0.01 × v² = 4 × 10⁻⁶ × 277229.92
v² = 2 × 4 × 10⁻⁶ × 277229.92/0.01
v = √(221.783936)
v = 14.89 m/s
Read more about point charges at;https://brainly.com/question/13914561
