A charge of −4.36 µC is located at the origin, and a charge of −4.15 µC is located along the y axis at 1.58744?
A charge of −4.36 µC is located at the origin,
and a charge of −4.15 µC is located along the
y axis at 1.58744 m.
At what point along the y-axis is the electric
field zero? The value of the Coulomb constant
is 8.99 × 10
9
N · m2
/C
2
.
Answer in units of m
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Answer … 0.804 m …
… - k Q₁ / y₁ ² + k Q₂ / y₂² = 0 … y₁ + y₂ = 1.58744 …
… so that … y₂ = 1.58744 - y₁ … therefore …
… Q₁ / y₁ ² = Q₂ / y₂² = Q₂ / ( 1.58744 - y₁ ) ² …
… ( 1.58744 - y₁ ) ² = Q₂ y₁ ² / Q₁ = 4.15 y₁ ² / 4.36 …
… 2.519966 – 3.17488 y₁ + y₁² = ( 0.951835 ) y₁ ²
… ( 0.048165 ) y₁ ² – 3.17488 y₁ + 2.519966 = 0
… solving for y₁ using the quadratic formula, we get …
… y₁ = 0.804