Two spherical objects are separated by a distance of 1.41 × 10^-3 m. The objects are initially electrically neutral and are very small compared to the distance between them. Each object acquires the same negative charge due to the addition of electrons. As a result, each object experiences an electrostatic force that has a magnitude of 1.40 × 10^-20 N. How many electrons did it take to produce the charge on one of the objects?
#'s 1 and 2 in Related Questions are nearly identical, the numbers are different, but the formula is what counts.
To find out how many electrons it took to produce the charge on one of the objects, we can use the equation for the electric force between two charged objects:
F = k * (|q1| * |q2|) / r^2
where F is the magnitude of the electrostatic force, k is the electrostatic constant (9.0 x 10^9 N m^2/C^2), q1 and q2 are the charges on the two objects, and r is the distance between the centers of the two objects.
In this case, both objects have acquired the same negative charge, so we can call their charges q1 and q2.
According to the problem, the magnitude of the electrostatic force is 1.40 x 10^-20 N, and the distance between the objects is 1.41 x 10^-3 m.
Plugging in these values into the equation, we get:
1.40 x 10^-20 N = (9.0 x 10^9 N m^2/C^2) * (|q1| * |q2|) / (1.41 x 10^-3 m)^2
Now, we can rearrange the equation to solve for the product of the two charges, |q1| * |q2|:
|q1| * |q2| = (1.40 x 10^-20 N) * [(1.41 x 10^-3 m)^2 / (9.0 x 10^9 N m^2/C^2)]
Calculating this expression, we find:
|q1| * |q2| ≈ 2.77 x 10^-36 C^2
Since both objects acquired the same negative charge, we can call this charge q.
So, q^2 = 2.77 x 10^-36 C^2, which means that:
q ≈ ±1.66 x 10^-18 C
Now, to find the number of electrons, we need to convert the charge q to the number of elementary charges (electron charge).
The elementary charge is approximately 1.6 x 10^-19 C.
Thus, the number of electrons is given by:
Number of electrons = q / elementary charge
Number of electrons ≈ (±1.66 x 10^-18 C) / (1.6 x 10^-19 C)
Calculating this expression, we find:
Number of electrons ≈ ±10.4
Therefore, it took approximately 10.4 electrons to produce the charge on one of the objects.