Two tiny, spherical water drops, with identical charges of -7.10 x 10-16 C, have a center-to-center separation of 1.23 cm. (a) What is the magnitude of the electrostatic force acting between them? (b) How many excess electrons are on each drop, giving it its charge imbalance?
k =9•10^9 N•m²/C²
F=k•q1•q2/r²= k•q²/r².
N=Q/e=7.1•10^-16/1.6•10^-19=4431
To find the magnitude of the electrostatic force between two charged spheres, we can use Coulomb's law. Coulomb's law states that the electrostatic force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between their centers.
(a) To find the magnitude of the electrostatic force between the water drops, we need to calculate:
1. The product of their charges (q1 * q2): Since both drops have identical charges, their product would be (-7.10 x 10^(-16) C) * (-7.10 x 10^(-16) C) = 5.044 x 10^(-31) C^2.
2. The square of the distance between their centers (r^2): The given center-to-center separation is 1.23 cm, which is 0.0123 meters. Therefore, the square of the distance would be (0.0123 m)^2 = 1.5129 x 10^(-4) m^2.
Now, we can plug these values into Coulomb's law:
Electrostatic force (F) = (k * q1 * q2) / (r^2)
where k is the electrostatic constant, approximately equal to 9 x 10^9 N m^2/C^2.
Substituting the values:
F = (9 x 10^9 N m^2/C^2) * (5.044 x 10^(-31) C^2) / (1.5129 x 10^(-4) m^2)
Calculating this expression will give you the magnitude of the electrostatic force between the water drops.
(b) To determine the number of excess electrons on each drop, we need to understand that the charge of an electron is -1.6 x 10^(-19) C.
The excess electrons on each drop can be calculated using the equation:
Number of excess electrons = (charge on the drop) / (charge of an electron)
Substituting the values:
Number of excess electrons = (-7.10 x 10^(-16) C) / (-1.6 x 10^(-19) C)
Calculating this expression will give you the number of excess electrons on each drop.