Two charged spheres are held a distance, r, apart. One sphere has a charge of +3μC, and the other sphere has a charge of +9μC. Compare the force of the +3μC sphere on the +9μC sphere with the force of the +9μC sphere on the +3μC sphere.
To compare the force between the two charged spheres, we can use Coulomb's Law. Coulomb's Law states that the force between two charged objects is directly proportional to 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 charged objects
k is the electrostatic constant (approximately 9 × 10^9 Nm^2/C^2)
q1 and q2 are the charges of the two objects
r is the distance between the two objects
In this case, let's denote the +3μC sphere as q1 and the +9μC sphere as q2. Since we want to compare the forces, we need to find the ratio of the two forces.
First, let's calculate the force of the +3μC sphere on the +9μC sphere:
F1 = k * (q1 * q2) / r^2
Substituting the values:
F1 = (9 × 10^9 Nm^2/C^2) * (3 × 10^-6 C) * (9 × 10^-6 C) / r^2
Next, let's calculate the force of the +9μC sphere on the +3μC sphere:
F2 = k * (q1 * q2) / r^2
Substituting the values:
F2 = (9 × 10^9 Nm^2/C^2) * (9 × 10^-6 C) * (3 × 10^-6 C) / r^2
Now, we can compare the two forces by finding their ratio:
F1 / F2 = [(9 × 10^9 Nm^2/C^2) * (3 × 10^-6 C) * (9 × 10^-6 C) / r^2] / [(9 × 10^9 Nm^2/C^2) * (9 × 10^-6 C) * (3 × 10^-6 C) / r^2]
Simplifying the expression:
F1 / F2 = (3 × 10^-6 C * 9 × 10^-6 C) / (9 × 10^-6 C * 3 × 10^-6 C)
The charges cancel each other out, leaving:
F1 / F2 = 1
Therefore, the force of the +3μC sphere on the +9μC sphere is equal to the force of the +9μC sphere on the +3μC sphere.