A small cork with an excess charge of +7.0 µC
is placed 0.16 m from another cork, which
carries a charge of −3.2 µC.
What is the magnitude of the electric force
between the corks? The Coulomb constant is
8.98755 × 10
9
N · m2
/C
2
.
Answer in units of N
To find the magnitude of the electric force between the corks, we can use Coulomb's Law. Coulomb's Law states that the magnitude of the electric 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 magnitude of the electric force,
- k is the Coulomb constant (8.98755 × 10^9 N · m^2 / C^2),
- |q1| and |q2| are the magnitudes of the charges of the two objects, and
- r is the distance between the two objects.
In this case, we have:
- |q1| = +7.0 µC = 7.0 × 10^-6 C (charge of the small cork)
- |q2| = -3.2 µC = -3.2 × 10^-6 C (charge of the other cork)
- r = 0.16 m (distance between the corks)
Plugging these values into the formula, we get:
F = (8.98755 × 10^9 N · m^2 / C^2) * [(7.0 × 10^-6 C) * (-3.2 × 10^-6 C)] / (0.16 m)^2
Simplifying the expression, we have:
F = (8.98755 × 10^9 N · m^2 / C^2) * (7.0 × 10^-6 C) * (-3.2 × 10^-6 C) / (0.16 m)^2
Calculating this expression using a calculator, we find:
F ≈ -2.114 N
Therefore, the magnitude of the electric force between the corks is approximately 2.114 N. Note that the negative sign indicates that the force is attractive.