A glass rod rubbed against your hair gains a charge of -14.0 nC. What is the electric force between the balloon and your hair when the two are separated by a distance of 7.1 cm? (Assume that the charges are located at a point.)

Hughicdg

To find the electric force between the balloon and your hair, we can use Coulomb's Law. Coulomb's Law states that the electric force between two charges 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 electric force between the charges,
k is Coulomb's constant (k ≈ 9 x 10^9 N m^2/C^2),
q1 and q2 are the charges, and
r is the distance between the charges.

In this case, the charge of the glass rod (-14.0 nC) will be one of the charges, and your hair will be the other charge. Since the charge of your hair is not given, we'll assume it is positive to feel the attraction from the negative charge on the glass rod.

Let's assume the charge on your hair is q2.

Now, we need to convert the charge of the glass rod to coulombs since the unit for Coulomb's constant is C (Coulombs).

1 nC (nanocoulomb) = 1 x 10^-9 C (coulomb)

Therefore, -14.0 nC = -14.0 x 10^-9 C

Now, we can plug the values into the formula:

F = k * (q1 * q2) / r^2

F = (9 x 10^9 N m^2/C^2) * (-14.0 x 10^-9 C * q2) / (0.071 m)^2

Simplifying further:

F = -126 * 10^-9 * q2 / 0.005041 m^2

F = -2.504 * 10^-5 * q2 N

So, the electric force between the balloon and your hair is approximately -2.504 * 10^-5 times the charge of your hair, given in Newtons (N). Note that the negative sign indicates an attractive force since the charges have opposite signs.

Since we don't have the charge of your hair, we cannot calculate the exact force. You would need to know the charge of your hair to find the numeric value of the electric force.