When point charges q1=+8.4uC and q2=+5.6uC are brought near each other, each experiences a repulsive force of magnitude 0.66N. Determine the distance between the charges.
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0.801m
To determine the distance between the charges, we can use Coulomb's Law:
F = (k * |q1 * q2|) / r²
Where:
F is the force between the charges,
k is the electrostatic constant (8.99 x 10^9 Nm²/C²),
q1 and q2 are the magnitudes of the charges, and
r is the distance between the charges.
Given:
q1 = +8.4 μC = 8.4 x 10^-6 C
q2 = +5.6 μC = 5.6 x 10^-6 C
F = 0.66 N
Plugging in these values into Coulomb's Law equation:
0.66 = (8.99 x 10^9 * |8.4 x 10^-6 * 5.6 x 10^-6|) / r²
Simplifying:
0.66 = (8.99 x 10^9 * 47.04 x 10^-12) / r²
0.66 = (42.1996 x 10^-3) / r²
r² = (42.1996 x 10^-3) / 0.66
r² = (42.1996 / 0.66) x 10^-3
r² = 63.9394 x 10^-3
r = √(63.9394 x 10^-3)
r ≈ 0.25 m
Therefore, the distance between the charges is approximately 0.25 meters.
To determine the distance between the charges, we can make use of Coulomb's law, which states that the magnitude of the electrostatic force between two point charges is given by:
F = (k * |q1 * q2|) / r^2
Where:
- F is the magnitude of the electrostatic force
- k is the electrostatic constant (k = 9 x 10^9 Nm^2/C^2)
- q1 and q2 are the magnitudes of the charges
- r is the distance between the charges
In this case, we are given that the magnitude of the repulsive force F is 0.66 N, q1 = +8.4 µC, q2 = +5.6 µC, and we need to find the distance r.
Rearranging the equation, we have:
r^2 = (k * |q1 * q2|) / F
Substituting the given values, we get:
r^2 = (9 x 10^9 Nm^2/C^2 * |(+8.4 µC) * (+5.6 µC)|) / (0.66 N)
Solving the equation, we find:
r^2 = (9 x 10^9 Nm^2/C^2 * 8.4 µC * 5.6 µC) / 0.66 N
Simplifying further, we have:
r^2 = 8.4 µC * 5.6 µC * (9 x 10^9 Nm^2/C^2) / 0.66 N
r^2 = 8.4 µC * 5.6 µC * (9 x 10^9 Nm^2/C^2) / (0.66 N)
Plugging in the values and evaluating the expression, we find:
r^2 ≈ 160000000
Taking the square root of both sides, we get:
r ≈ 12649.11 meters
Therefore, the distance between the charges is approximately 12649.11 meters.