φ₁ = k * q₁ / x
φ₂ = k * q₂ / (r - x)
φ₁ + φ₂ = 0
k * q₁ / x + k * q₂ / (r - x) = 0 => k * q₁ / x = - k * q₂ / (r - x)
q₁ / x = - q₂ / (r - x)
q₁ * (r - x) = - q₂ * x
q₁ * r - q₁ * x = - q₂ * x
q₂ * x - q₁ * x = - q₁ * r
x * (q₂ - q₁) = - q₁ * r
x = - q₁ * r / (q₂ - q₁)
x = - 4 нКл * 5 см / (- 16 нКл - 4 нКл) = 1 см - от 1-го заряда
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Verified answer
φ₁ = k * q₁ / x
φ₂ = k * q₂ / (r - x)
φ₁ + φ₂ = 0
k * q₁ / x + k * q₂ / (r - x) = 0 => k * q₁ / x = - k * q₂ / (r - x)
q₁ / x = - q₂ / (r - x)
q₁ * (r - x) = - q₂ * x
q₁ * r - q₁ * x = - q₂ * x
q₂ * x - q₁ * x = - q₁ * r
x * (q₂ - q₁) = - q₁ * r
x = - q₁ * r / (q₂ - q₁)
x = - 4 нКл * 5 см / (- 16 нКл - 4 нКл) = 1 см - от 1-го заряда