What is the repulsive force between two pith balls that are 12.0 cm apart and have equal charges of -39.0 nC?
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To calculate the repulsive force between two charged pith balls, we can use Coulomb's Law. Coulomb's Law states that the force between two charges is directly proportional to the product of their magnitudes 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 the electrostatic constant (k = 8.99 x 10^9 Nm^2/C^2),
q1 and q2 are the magnitudes of the charges,
r is the distance between the charges.
In this case, both pith balls have equal charges, so q1 = q2 = -39.0 nC. The distance between them is given as 12.0 cm, which is equivalent to 0.12 m.
Plugging in the values into the formula, we have:
F = (8.99 x 10^9 Nm^2/C^2) * ((-39.0 nC) * (-39.0 nC)) / (0.12 m)^2
Now let's calculate the force:
To determine the repulsive force between two charged objects, 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.
Coulomb's law equation is:
F = k * (|Q1| * |Q2|) / r^2
Where:
F is the force between the two charges,
k is the electrostatic constant (k = 8.99 x 10^9 Nm^2/C^2),
|Q1| and |Q2| are the magnitudes of the charges, and
r is the distance between the charges.
Let's calculate the repulsive force between the two pith balls.
Given data:
|Q1| = |Q2| = 39.0 nC (both charges are the same magnitude and negative)
r = 12.0 cm = 0.12 m (convert cm to meters)
Plugging these values into the formula:
F = (8.99 x 10^9 Nm^2/C^2) * ((39.0 x 10^-9 C) * (39.0 x 10^-9 C)) / (0.12 m)^2
Simplifying the equation:
F = (8.99 x 10^9 Nm^2/C^2) * (1521 x 10^-18 C^2) / 0.0144 m^2
F = (8.99 x 10^9 Nm^2/C^2) * (1.521 x 10^-15 C^2) / 0.0144 m^2
F = (8.99 x 1.521 x 10^-6 N) / (0.0144)
F ≈ 0.949 N
Therefore, the repulsive force between the two pith balls is approximately 0.949 N.