In a vacuum, two particles have charges of q1 and q2, where q1 = +3.8C. They are separated by a distance of 0.37 m, and particle 1 experiences an attractive force of 4.7 N. What is the value of q2, with its sign?
Two spherical objects are separated by a distance of 1.45 × 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 1.58 × 10-20 N. How many electrons did it take to produce the charge on one of the objects?
To find the value of q2 in the first question, we can use Coulomb's Law, which states that the force between two charged particles is 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 particles,
- k is the Coulomb's constant (approximately 9 x 10^9 N⋅m^2/C^2),
- |q1| and |q2| are the magnitudes of the charges of particles 1 and 2 (in Coulombs),
- r is the separation distance between the particles (in meters).
In this case, we are given the following information:
- q1 = +3.8C (positive charge)
- r = 0.37 m
- F = 4.7 N (attractive force)
First, let's find the magnitude of q2. Rearranging the formula, we have:
|q2| = (F * r^2) / (k * |q1|)
Substituting the given values:
|q2| = (4.7 N * (0.37 m)^2) / (9 x 10^9 N⋅m^2/C^2 * 3.8C)
Simplifying the equation gives:
|q2| ≈ 3.849 x 10^-9 C
Now, to find the sign of q2, we know that the particles experience an attractive force. Since q1 is positive, q2 must be negative to attract particle 1. Therefore, the value of q2 is approximately -3.849 x 10^-9 C.
-----------------------------------------------------------------------------------------------------------------
To find the number of electrons in the second question, we can use the fact that each electron carries a charge of -1.6 x 10^-19 C.
The formula for the force between two charged objects is the same as Coulomb's Law:
F = k * (|q1| * |q2|) / r^2
In this case, both objects have acquired the same negative charge, so let's represent the magnitude of the charge on each object as |q|. We are given the following information:
r = 1.45 x 10^-3 m
F = 1.58 x 10^-20 N
Using the same formula as before:
|q| = (F * r^2) / (k * |q|)
|q| ≈ (1.58 x 10^-20 N * (1.45 x 10^-3 m)^2) / (9 x 10^9 N⋅m^2/C^2)
Simplifying the equation gives:
|q| ≈ 2.635 x 10^-19 C
Now, to find the number of electrons, we need to divide the charge |q| by the charge per electron:
Number of electrons = |q| / (-1.6 x 10^-19 C)
Number of electrons ≈ (2.635 x 10^-19 C) / (-1.6 x 10^-19 C)
Number of electrons ≈ -1.647
Since the number of electrons cannot be negative, we can approximate the number of electrons to 2 (ignoring the fractional part).
Therefore, it took approximately 2 electrons to produce the charge on one of the objects.