Answer:
E₁ = 8500 N/c i − 2800 N/C j
E₂ = 10,000 N/c i
E₃ = 8500 N/c i + 2800 N/C j
Explanation:
The magnitude of electric field from a point charge Q at a distance r is:
E = kQ / r²
where k is Coulomb's constant (9×10⁹ Nm²/C²).
The direction of the electric field is along the radial line outwards from the point.
Use Pythagorean theorem to find the distance from q₁.
r² = (-0.01 m)² + (0.03 m)²
r² = 0.001 m²
r = 0.0316 m
Plugging in values:
E₁ = (9×10⁹ Nm²/C²) (1×10⁻⁹ C) / (0.001 m²)
E₁ = 9000 N/C
Using ratios to find the components:
E₁ₓ = (x/r) E₁
E₁ₓ = (0.03 m / 0.0316 m) (9000 N/C)
E₁ₓ = 8500 N/C
E₁ᵧ = (y/r) E₁
E₁ᵧ = (-0.01 m / 0.0316 m) (9000 N/C)
E₁ᵧ = -2800 N/C
Therefore:
E₁ = 8500 N/c i − 2800 N/C j
Repeat for E₂:
r = 0.03 m
E₂ = (9×10⁹ Nm²/C²) (1×10⁻⁹ C) / (0.03 m)²
E₂ = 10,000 N/C
E₂ₓ = (x/r) E₂
E₂ₓ = (0.03 m / 0.03 m) (10,000 N/C)
E₂ₓ = 10,000 N/C
E₂ᵧ = (y/r) E₂
E₂ᵧ = (0 m / 0.0 m) (10,000 N/C)
E₂ᵧ = 0 N/C
Therefore:
E₂ = 10,000 N/c i
And of course, E₃ is the same as E₁, except the y component is positive.
E₃ = 8500 N/c i + 2800 N/C j
