Suppose two thin flat plates measure 3.5m x 3.5m and are separated by 6.5mm. They are oppositely charged with +-20microCoulombs. Estimate the total force exerted by one plate on the other (ignore edge effects).
Well, I must admit, those plates are quite "charged" to be in such a close relationship! It seems like they are really attracted to each other, just like two magnets running towards each other on a honeymoon vacation. Let's calculate this electrifying force!
Now, to estimate the total force, we can use Coulomb's law. Coulomb's law states that the force between two charged plates is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
So, we have the following information:
Charge of Plate 1 (Q1) = +20 microCoulombs = 20 × 10^(-6) Coulombs
Charge of Plate 2 (Q2) = -20 microCoulombs = -20 × 10^(-6) Coulombs
Distance between the plates (d) = 6.5 mm = 6.5 × 10^(-3) meters
Using Coulomb's law, the formula for the force (F) between the plates is:
F = (k * |Q1 * Q2|) / d^2
Where k is the electrostatic constant (k ≈ 9 × 10^9 N m^2/C^2).
Plugging in the values, we get:
F = (9 × 10^9 * |20 × 10^(-6) * -20 × 10^(-6)|) / (6.5 × 10^(-3))^2
Calculating that, we find:
F ≈ 0.00854 Newtons
So, the approximate total force exerted by one plate on the other is around 0.00854 Newtons. That's quite a shocking force! I hope they can stop sparking and work things out peacefully instead.
To estimate the total force exerted by one plate on the other, we can use the formula for the force between two charged plates:
F = (Q1 * Q2) / (4 * π * ε * d^2)
Where:
F is the force between the plates,
Q1 and Q2 are the charges on the plates,
ε is the permittivity of free space (ε = 8.854 x 10^-12 C^2 / N m^2),
and d is the distance between the plates.
Given that Q1 = Q2 = ±20 μC = ±20 x 10^-6 C, and d = 6.5 mm = 6.5 x 10^-3 m, we can plug these values into the formula:
F = (20 x 10^-6 C)^2 / (4 x π x 8.854 x 10^-12 C^2 / N m^2 x (6.5 x 10^-3 m)^2)
F = (400 x 10^-12 C^2) / (4 x 3.1416 x 8.854 x 10^-12 C^2 / N m^2 x (6.5 x 10^-3 m)^2)
F = (400 x 10^-12) / (4 x 3.1416 x 8.854 x (6.5 x 10^-3)^2 N)
Evaluating this expression, we find:
F ≈ 3.156 x 10^-5 N
Therefore, the estimated total force exerted by one plate on the other is approximately 3.156 x 10^-5 Newtons.
To estimate the total force exerted by one plate on the other, we can use Coulomb's Law. Coulomb's Law states that the 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 force between the two charges,
k is the electrostatic constant (k ≈ 9 × 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 charges q1 and q2 are +-20 microCoulombs (±20 μC). To use Coulomb's Law, we need to convert the charges to Coulombs by dividing by 1,000,000: q1 = q2 = ±20 * 10^-6 C.
The distance between the plates is given as 6.5 mm (millimeters). To use Coulomb's Law, we need to convert the distance to meters by dividing by 1000: r = 6.5 * 10^-3 m.
Now we can substitute these values into the equation and calculate the force:
F = (k * q1 * q2) / r^2
F = (9 * 10^9 N * m^2 / C^2) * (±20 * 10^-6 C) * (±20 * 10^-6 C) / (6.5 * 10^-3 m)^2
To calculate the force, we need to substitute the appropriate signs for the charges. Since the plates are oppositely charged, we consider one charge positive and the other negative. Let's assume that q2 is positive, and q1 is negative.
F = (9 * 10^9 N * m^2 / C^2) * (20 * 10^-6 C) * (-20 * 10^-6 C) / (6.5 * 10^-3 m)^2
Now, we can calculate the force using a calculator:
F ≈ -6.09 N
Therefore, the estimated total force exerted by one plate on the other is approximately 6.09 Newtons in the opposite direction.
http://www.youtube.com/watch?v=7NUbsQt-G9U&feature=player_embedded#!
watch the first 3 min. Great Professor friend of mine.