A point charge q1 has a magnitude of 3x10^-6 C and a second charge q2 has a magnitude of -1.5x10^-6 C and is located 0.12 meters from the first charge. Determine the type and magnitude of electrostatic force each charge exerts on each other.
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To solve this math problem, we can use Coulomb's Law, which states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
Given data:
q1 = 3x10^-6 C
q2 = -1.5x10^-6 C
r = 0.12 m
First, we need to calculate the electrostatic force (F) exerted by q1 on q2, and then the force exerted by q2 on q1.
Using the formula:
F = k * (|q1| * |q2|) / r^2,
where k is the electrostatic constant (k = 9x10^9 N m^2/C^2), |q1| is the magnitude of q1, |q2| is the magnitude of q2, and r is the distance between the charges, we can plug in the values:
F1 = (9x10^9 N m^2/C^2) * (|3x10^-6 C| * |-1.5x10^-6 C|) / (0.12 m)^2
F1 = (9x10^9 N m^2/C^2) * (4.5x10^-12 C^2) / (0.0144 m^2)
F1 = 3.85714286x10^-3 N
Now, let's calculate the electrostatic force (F) exerted by q2 on q1:
F2 = (9x10^9 N m^2/C^2) * (|-1.5x10^-6 C| * |3x10^-6 C|) / (0.12 m)^2
F2 = (9x10^9 N m^2/C^2) * (4.5x10^-12 C^2) / (0.0144 m^2)
F2 = 3.85714286x10^-3 N
Therefore, the electrostatic force exerted by q1 on q2 is 3.85714286x10^-3 Newtons (N), and the electrostatic force exerted by q2 on q1 is also 3.85714286x10^-3 N. Both forces have the same magnitude.
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