Assuming equal point charges, calculate the magnitude of the charge in C if the electrostatic force is great enough to support the weight of a 1.95 mg piece of tape held 1.05 cm above another?
To calculate the magnitude of the charge, we need to use Coulomb's law. Coulomb's law states that the force between two point 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 electrostatic force,
k is the electrostatic constant (9.0 x 10^9 Nā
m^2/C^2),
q1 and q2 are the charges of the two objects, and
r is the distance between them.
In this case, the electrostatic force (F) is equal to the weight of the tape, which can be calculated using the equation:
F = m * g
where:
m is the mass of the tape (1.95 mg) and
g is the acceleration due to gravity (approximately 9.8 m/s^2).
First, let's convert the mass of the tape from milligrams (mg) to kilograms (kg):
m = 1.95 mg = 1.95 x 10^-6 kg
Next, we need to convert the distance between the charges from centimeters (cm) to meters (m):
r = 1.05 cm = 1.05 x 10^-2 m
Now we can calculate the electrostatic force using the weight equation:
F = m * g = (1.95 x 10^-6 kg) * (9.8 m/s^2)
Once we have the value for F, we can rearrange Coulomb's law to solve for the charge (q1 or q2):
q1 (or q2) = (F * r^2) / (k * q2 (or q1))
Since we have equal point charges, we can assume q1 = q2.
Therefore, we can rewrite the equation as:
q = (F * r^2) / (k * q)
We can rearrange the equation to solve for q:
q = (F * r^2) / (k)
Now, let's plug in the values we have:
q = [(1.95 x 10^-6 kg) * (9.8 m/s^2) * (1.05 x 10^-2 m)^2] / (9.0 x 10^9 Nā
m^2/C^2)
Calculating this expression will give us the magnitude of the charge in coulombs (C).