A balloon rubbed against denim gains a charge of -9 µC. What is the electric force between the balloon and the denim when the two are separated by a distance of 5 cm.
To calculate the electric force between the balloon and the denim, we can use the formula for the electric force between two charges:
F = (k * |q1 * q2|) / r^2
Where:
- F is the electric force
- k is the Coulomb constant, approximately equal to 9 * 10^9 N * m^2 / C^2
- q1 and q2 are the charges of the two objects
- r is the distance between the two objects.
In this case, the charge of the balloon is -9 µC, which we'll convert to coulombs by multiplying by 10^-6:
q1 = -9 µC * 10^-6 C/µC = -9 * 10^-6 C
Since the balloon gains this negative charge, the denim would have an equal and opposite positive charge.
q2 = 9 * 10^-6 C
The distance between the balloon and the denim is 5 cm, which we'll convert to meters by multiplying by 10^-2:
r = 5 cm * 10^-2 m/cm = 5 * 10^-2 m
Now, we can substitute these values into the formula and calculate the electric force:
F = (9 * 10^9 N * m^2 / C^2) * (|(-9 * 10^-6 C) * (9 * 10^-6 C)|) / (5 * 10^-2 m)^2
F = (9 * 10^9 N * m^2 / C^2) * (81 * 10^-12 C^2) / (25 * 10^-4 m^2)
F = (9 * 81) * (10^9 * 10^-12 * 10^-4) * (N * m * m / C * C)
F = 729 * 10^-7 * N
F = 7.29 * 10^-5 N
Therefore, the electric force between the balloon and the denim when they are separated by a distance of 5 cm is approximately 7.29 * 10^-5 Newtons (N).