11. An object with a charge of +6.0 µC is 0.30 m from a second object and experiences an attractive force of 1.80 N. What is the magnitude of the charge on the second object? (µC = 1.0 × 10-6 C) (Answer: -3.0 µC)
Can someone please explain how to do this problem? I don't just want the answer, but i need to know the correct way to calculate it.
F=k•q₁•q₂/r²,
k =9•10⁹ N•m²/C²,
q₂ = F•r²/k•q₁ = 1.8•0.3²/9•10⁹•6•10⁻⁶ =
=3•10⁻⁶ C = 3 μC
Due to the attraction of the charges
q₂ = - 3 μC
To solve this problem, we can use Coulomb's Law, which states that the force between two charged objects 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 objects, k is the electrostatic constant (approximately 9 × 10^9 N m^2/C^2), q1 and q2 are the charges of the objects, and r is the distance between them.
In this problem, we are given the following information:
q1 = +6.0 µC = +6.0 × 10^-6 C
F = 1.80 N
r = 0.30 m
k = 9 × 10^9 N m^2/C^2
q2 = ?
We can rearrange the formula to solve for q2:
q2 = (F * r^2) / (k * q1)
Plugging in the given values:
q2 = (1.80 N * (0.30 m)^2) / (9 × 10^9 N m^2/C^2 * +6.0 × 10^-6 C)
Calculating this equation will give us the magnitude of the charge on the second object.