Final answer:
To find the charge on each object, we use Coulomb's Law. After converting the distance to meters, we plug in the given force and constants and then take the square root to solve for the charge. The charge magnitude will be expressed in Coulombs (C).
Step-by-step explanation:
The question asks to calculate the magnitude of the charge on each of two identical objects that repel each other with a force of 7.158 n when they are separated by a distance of 5.00 cm. To solve this, we will use Coulomb's Law which states that the magnitude of the electrostatic force of interaction between two point charges is directly proportional to the scalar multiplication of the magnitudes of 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 charges,
- k is Coulomb's constant (8.9875×10^9 N⋅m²/C²),
- q1 and q2 are the magnitudes of the charges,
- r is the distance between the charges in meters.
Since the charges are identical q1 = q2, and we can denote both charges simply as q. By rearranging the formula and solving for q we get:
q = √(F * r^2 / k)
Let's convert 5.00 cm to 0.05 meters and plug all the values into the equation:
q = √(7.158×10^-9 N * (0.05 m)^2 / (8.9875×10^9 N⋅m²/C²))
After calculating, we find the magnitude of the charge on each object. Remember to keep in mind the units of your answer should be in Coulombs (C).