Refer to the figure shown below.
Charge q₁ = 0.5 nC = 0.5x10⁻⁹ C
Charge q₂ = 8 nC = 8x10⁻⁹ C
d = 1.2 m, the distance between the two charges.
x is the distance between the two charges, measured from the charge q₁.
From Coulomb's Law,
The electric field generated along x by q₁ is
E₁ = k(q₁/x²)
The electric field generated along x by q₂ is
E₂ = -k[q₂/(d-x)²]
where
k = 8.988x10⁹ (N-m²)/C² is the Coulomb constant/
When the electric field along x is zero, then
E₁ + E₂ = 0
k[q₁/x² - q₂/(d-x)²] = 0
That is,
0.5/x² = 8/(1.2 - x)²
8x² = 0.5(1.2 - x)²
16x² = 1.44 - 2.4x + x²
15x² + 2.4x - 1.44 = 0
Solve with the quadratic formula.
x = (1/30)*[-2.4 +/- √(5.76 + 86.4)]
= 0.24 or -0.4 m
Reject the negative answer to obtain
x = 0.24 m
d-x = 0.96 m
Answer
The electric field is zero between the charges so that
(a) It is at 0.24 m from the 0.5 nC charge, and
(b) It is at 0.96 m from the 8 nC charge.
Charge q₁ = 0.5 nC = 0.5x10⁻⁹ C
Charge q₂ = 8 nC = 8x10⁻⁹ C
d = 1.2 m, the distance between the two charges.
x is the distance between the two charges, measured from the charge q₁.
From Coulomb's Law,
The electric field generated along x by q₁ is
E₁ = k(q₁/x²)
The electric field generated along x by q₂ is
E₂ = -k[q₂/(d-x)²]
where
k = 8.988x10⁹ (N-m²)/C² is the Coulomb constant/
When the electric field along x is zero, then
E₁ + E₂ = 0
k[q₁/x² - q₂/(d-x)²] = 0
That is,
0.5/x² = 8/(1.2 - x)²
8x² = 0.5(1.2 - x)²
16x² = 1.44 - 2.4x + x²
15x² + 2.4x - 1.44 = 0
Solve with the quadratic formula.
x = (1/30)*[-2.4 +/- √(5.76 + 86.4)]
= 0.24 or -0.4 m
Reject the negative answer to obtain
x = 0.24 m
d-x = 0.96 m
Answer
The electric field is zero between the charges so that
(a) It is at 0.24 m from the 0.5 nC charge, and
(b) It is at 0.96 m from the 8 nC charge.