Calculate the electrical force (in Newtons) exerted between a 22-gram balloon with a charge of -2.6 µC and a wool sweater with a charge of +3.8 µC; the separation distance is 0.75 m.
To calculate the electrical force between the balloon and the sweater, we can use Coulomb's Law. Coulomb's Law states that the electrical 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 electrical force between the two charges
- k is the electrostatic constant (k ≈ 8.99 x 10^9 N m^2 / C^2)
- q1 and q2 are the charges of the two objects
- r is the separation distance between the two objects
Let's plug in the given values into the formula:
F = (8.99 x 10^9 N m^2 / C^2) * ((-2.6 x 10^-6 C) * (3.8 x 10^-6 C)) / (0.75 m)^2
Now, let's calculate it:
F ≈ (8.99 x 10^9 N m^2 / C^2) * (-9.88 x 10^-12 C^2) / (0.5625 m^2)
F ≈ -8.88 x 10^-2 N
Therefore, the electrical force between the balloon and the sweater is approximately -8.88 x 10^-2 Newtons. Note that the negative sign indicates that the forces are repelling each other.