A charge of -5.4X10^-7 exerts an upward .250 N force on an unknown charge .260m directly below it. What is the unknown charge?
F=k•q₁•q₂/r²
k =9•10⁹ N•m²/C²
q₂ =F•r²/k •q₁
To find the unknown charge, we can use Coulomb's law, which states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
We are given:
- The charge of -5.4 × 10^-7 C (Coulombs)
- The force exerted of 0.250 N (Newtons)
- The distance between the charges of 0.260 m
Coulomb's law can be written as:
F = k * (|q1 * q2|) / r^2
where:
F is the force between the charges
k is the electrostatic constant (k = 8.99 × 10^9 N·m^2/C^2)
|q1| and |q2| are the magnitudes of the charges
r is the distance between the charges
Rearranging the formula, we can solve for |q2| (the magnitude of the unknown charge):
|q2| = (F * r^2) / (k * |q1|)
Substituting the values, we have:
|q2| = (0.250 N * (0.260 m)^2) / (8.99 × 10^9 N·m^2/C^2 * 5.4 × 10^-7 C)
Simplifying the expression, we get:
|q2| ≈ 1.63 × 10^-6 C
Therefore, the magnitude of the unknown charge is approximately 1.63 × 10^-6 Coulombs.