A) A small cork with an excess charge of +9.0x10^-6 is placed 0.13 m from another cork, which carries a charge of −3.2x10^-6. What is the magnitude of the electric force between the corks? The Coulomb constant is 8.98755 × 10^9 N • m^2/C^2. Answer in units of N
B)Is this force attractive or repulsive?
1. Unable to determine
2. Attractive
3. Repulsive
C) How many excess electrons are on the negative cork? Answer in units of electrons
D) How many electrons has the positive cork lost? Answer in units of electrons
Repulsive
A) To find the magnitude of the electric force between the corks, we can use the equation for the electric force between two charges:
F = (k * |q1 * q2|) / r^2
where F is the electric force, k is the Coulomb constant, q1 and q2 are the charges, and r is the distance between the charges.
Given:
Coulomb constant, k = 8.98755 × 10^9 N • m^2/C^2
q1 = 9.0x10^-6 C (charge of the small cork)
q2 = -3.2x10^-6 C (charge of the other cork)
r = 0.13 m
Substituting the values into the equation, we get:
F = (8.98755 × 10^9 * |9.0x10^-6 * -3.2x10^-6|) / (0.13)^2
F = (8.98755 × 10^9 * 2.88x10^-11) / 0.0169
F ≈ 1.53736 N
Therefore, the magnitude of the electric force between the corks is approximately 1.53736 N.
B) To determine if the force is attractive or repulsive, we need to observe the signs of the charges involved. In this case, the small cork has a positive charge (+9.0x10^-6 C), and the other cork has a negative charge (-3.2x10^-6 C). Opposite charges attract each other, so the force between them is attractive.
Therefore, the force is attractive (Option 2).
C) To find the number of excess electrons on the negative cork, we need to know the elementary charge, which is the charge on a single electron.
The elementary charge is e = 1.6x10^-19 C (approximately).
Given:
charge of the negative cork = -3.2x10^-6 C
To find the number of excess electrons, we can divide the negative charge by the elementary charge:
Number of excess electrons = (-3.2x10^-6 C) / (1.6x10^-19 C)
Number of excess electrons ≈ -2x10^13 electrons
Therefore, the negative cork has approximately 2x10^13 excess electrons.
D) To find the number of electrons the positive cork has lost, we can use the same approach.
Given:
charge of the positive cork = +9.0x10^-6 C
To find the number of electrons lost, we can divide the positive charge by the elementary charge:
Number of electrons lost = (9.0x10^-6 C) / (1.6x10^-19 C)
Number of electrons lost ≈ 5.625x10^13 electrons
Therefore, the positive cork has lost approximately 5.625x10^13 electrons.