suppose that resting on your non-conducting desktop is a tiny piece of paper (m=0.08g) that has a charge of 4x10^-10C. You bring your comb 3 cm away from it and the paper jumps up to the comb. Give an approximate value for the charge of the comb. Does the comb carry an excess of electrons or protons? How many?
To find the approximate value for the charge of the comb, we can use Coulomb's Law, which states that the electrostatic 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 equation for Coulomb's Law is: F = k * (q1 * q2) / r^2
Where:
F is the electrostatic force between the two charges,
k is the electrostatic constant (~9 * 10^9 N * m^2 / C^2),
q1 and q2 are the charges of the two objects, and
r is the distance between the charges.
In this case, we know the charge of the tiny piece of paper is 4x10^-10 C and the distance between the paper and the comb is 3 cm (which we'll convert to meters later). We want to find the charge of the comb.
Given:
q1 (paper) = 4x10^-10 C
q2 (comb) = ?
r = 0.03 m
Now, let's assume that the electrostatic force between the paper and the comb caused the paper to jump up to the comb. This means the force was attractive, indicating opposite charges on the paper and the comb.
Let's assume the comb carries an excess of electrons. Electrons have a negative charge, so the comb will have a negative charge. To find the number of electrons on the comb, we'll divide the charge of the comb (q2) by the elementary charge (e = 1.6x10^-19 C), which is the charge of a single electron.
Let's calculate the charge of the comb:
F = k * (q1 * q2) / r^2
Rearrange the equation to solve for q2 (comb's charge):
q2 = (F * r^2) / (k * q1)
Substituting the known values:
q2 = (F * (0.03)^2) / (9 * 10^9 * (4x10^-10))
Now, let's calculate the force between the paper and the comb. The force can be considered as the weight of the paper since it jumped up:
Force = weight = mass * gravitational acceleration
F = m * g
Given:
m (mass of the paper) = 0.08 g = 0.08 * 10^-3 kg
g (gravitational acceleration) ≈ 9.8 m/s^2
F = (0.08 * 10^-3) kg * 9.8 m/s^2
Now, substitute this force value back into the equation for q2 to find the charge of the comb:
q2 = [(0.08 * 10^-3) * 9.8 * (0.03)^2] / (9 * 10^9 * (4x10^-10))
Simplifying this expression will give us the approximate value for the charge of the comb.