wo objects each have a positive charge. The total charge on both objects is 365 µC. When the objects are placed a distance of 1.30 m apart, each exerts an electrostatic force of 24.3 N on the other. What is the charge on each object? (Give your answers in µC.)
To find the charge on each object, we can use Coulomb's Law, which states that the electrostatic force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Let's break down the given information:
- Total charge on both objects: 365 µC
- Distance between the objects: 1.30 m
- Electrostatic force between the objects: 24.3 N
To start, let's assume the charges on the objects as q1 and q2.
According to Coulomb's Law, we have the equation:
F = k * (|q1 * q2| / r^2)
where F is the electrostatic force, k is the electrostatic constant (9 x 10^9 Nm^2/C^2), q1 and q2 are the charges on the objects, and r is the distance between the objects.
Since the electrostatic force and the distance between the objects are given, we can rearrange the equation to solve for the product of the charges (q1 * q2):
q1 * q2 = (F * r^2) / k
Plugging in the values, we have:
q1 * q2 = (24.3 N * (1.30 m)^2) / (9 x 10^9 Nm^2/C^2)
Calculating the expression on the right-hand side gives us:
q1 * q2 = 4.52 x 10^-7 C^2
Since the charges on the objects are positive, we can conclude that q1 and q2 have the same sign. Thus, the charge on each object is the square root of the value we obtained:
q1 = q2 = √(4.52 x 10^-7 C^2)
Calculating the square root, the charge on each object is approximately 6.7277 x 10^-4 C, or 672.77 µC (rounded to five significant figures).
Therefore, the charge on each object is approximately 672.77 µC.