Final answer:
To solve this problem, we can use Coulomb's Law, which states that the 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. We can use the given force when the spheres are 4 cm apart to find the charge of each sphere. Then we can use the charge to calculate the force when the distance between the spheres is 5.6 cm.
Step-by-step explanation:
To solve this problem, we can use Coulomb's Law, which states that the 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. The formula for Coulomb's Law is:
F = k * (q1 * q2) / r^2
where F is the force, k is the Coulomb constant (approximately 9 * 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
In this problem, we are given that the force when the spheres are 4 cm apart is 0.003 N. We can use this information to find the charge of each sphere:
0.003 N = (k * (q1 * q2)) / (0.04 m)^2
Simplifying the equation, we get:
q1 * q2 = (0.003 N * (0.04 m)^2) / k
Using the charge of one sphere, we can find the force when the spheres are 5.6 cm apart:
F = (k * (q1 * q2)) / (0.056 m)^2
Plugging in the values and solving the equation, we can find the force:
F = (9 * 10^9 Nm^2/C^2 * (0.003 N * (0.04 m)^2) / k) / (0.056 m)^2
The force when the spheres are 5.6 cm apart is approximately 0.001 N.