In a vacuum, two particles have charges of q1 and q2, where q1 = +3.7 µC. They are separated by a distance of 0.22 m, and particle 1 experiences an attractive force of 3.5 N. What is q2 (magnitude and sign)?
force=kq1q2/distance^2 solve for q2. if the force on q1 is attractive, q2 has to be negative.
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To find the magnitude and sign of q2, we can use Coulomb's Law:
F = k * |q1 * q2| / r^2
Where:
F = attractive force between the particles
k = Coulomb's constant (k ≈ 9 * 10^9 N * m^2 / C^2)
q1 = charge of particle 1 (given as +3.7 µC, which is 3.7 * 10^-6 C)
q2 = charge of particle 2 (unknown)
r = distance between the particles (given as 0.22 m)
Rearranging Coulomb's Law formula:
q2 = (F * r^2) / (k * |q1|)
Substituting the given values:
q2 = (3.5 N * (0.22 m)^2) / (9 * 10^9 N * m^2 / C^2 * |3.7 * 10^-6 C|)
Simplifying:
q2 = (3.5 N * 0.0484 m^2) / (3.33 * 10^-3 C^2)
q2 = 0.1694 N * m^2 / C^2
Therefore, the magnitude of q2 is approximately 0.1694 N * m^2 / C^2.
Since particle 1 experiences an attractive force, the charges q1 and q2 must have opposite signs. Therefore, q2 is negative (-).
To find the magnitude and sign of q2, we can use Coulomb's law, which states that the force between two charged particles is proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's law is:
F = k * |q1 * q2| / r^2
Where:
F is the force between the particles
k is the electrostatic constant (9 × 10^9 N·m^2/C^2)
|q1| and |q2| are the magnitudes of the charges of particles 1 and 2, respectively
r is the distance between the particles
We are given the following information:
q1 = +3.7 µC (microCoulombs) = 3.7 × 10^(-6) C
r = 0.22 m
F = 3.5 N
Plugging in the values into Coulomb's law equation, we have:
3.5 N = (9 × 10^9 N·m^2/C^2) * |(3.7 × 10^(-6) C) * q2| / (0.22 m)^2
Simplifying the equation:
3.5 = (9 × 10^9) * (3.7 × 10^(-6)) * |q2| / (0.22)^2
Multiply both sides by (0.22)^2 to isolate |q2|:
(0.22)^2 * 3.5 = (9 × 10^9) * (3.7 × 10^(-6)) * |q2|
Solve for |q2|:
|q2| = ((0.22)^2 * 3.5) / ((9 × 10^9) * (3.7 × 10^(-6)))
Calculating this in a calculator, we find:
|q2| ≈ 2.121 × 10^(-8) C
Since we need the magnitude and sign of q2, we can conclude that q2 is approximately -2.121 × 10^(-8) C. The negative sign indicates an opposite charge compared to q1.