A balloon rubbed against denim gains a

charge of −5.0 µC.
What is the electric force between the
balloon and the denim when the two are
separated by a distance of 3.0 cm? (Assume
that the charges are located at a
point.) The value of the Coulomb constant is
8.98755 × 109 N · m2
/C
2
.
Include direction of the force.

To calculate the electric force between two charged objects, we can use Coulomb's Law, which states that the magnitude of the electric force is directly proportional to the product of the two 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 electric force between the objects,
- k is the Coulomb constant (k = 8.98755 × 10^9 N · m^2 / C^2),
- q1 and q2 are the charges of the objects (in this case, the balloon and denim),
- r is the distance between the charges.

Given:
- The charge of the balloon is -5.0 µC (or -5.0 × 10^-6 C),
- The charge of the denim is assumed to be 0 C (since it was not specified),
- The distance between the balloon and the denim is 3.0 cm (or 0.03 m),
- The Coulomb constant (k) is 8.98755 × 10^9 N · m^2 / C^2.

First, we need to convert the charge of the balloon to coulombs:

q1 = -5.0 × 10^-6 C

Now we can plug in the values into the Coulomb's Law equation:

F = (8.98755 × 10^9 N · m^2 / C^2 * |(-5.0 × 10^-6 C) * 0 C|) / (0.03 m)^2

Simplifying further:

F = (8.98755 × 10^9 N · m^2 / C^2 * 5.0 × 10^-6 C) / (0.03 m)^2

F = 1.49792 × 10^-2 N

The electric force between the balloon and the denim is approximately 0.0149 N.

As for the direction of the force, it depends on the sign of the charges. Since the balloon is negatively charged and the denim assumed to be neutral (zero charge), the electric force would be attractive, pulling the balloon towards the denim.

You should have payed attention in class.