Assume that in interstellar space the distance between two electrons is about 0.87 cm. The electric force between them are repulsive. Calculate the electric force between these two electrons. The value of the Coulomb constant 9 × 109 N · m2/C2 and the elemental charge is 1.6 × 10−19 C.
Part 2. Calculate the gravitational force between these two electrons. The universal gravitational constant is 6.7 × 10−11 N · m2/kg2 and the mass of the electron is 9 × 10−31 kg.
To calculate the electric force between two electrons, we can use Coulomb's Law equation:
Electric force = (Coulomb constant * Elemental charge^2) / (distance between electrons)^2
Given:
Coulomb constant (k) = 9 × 10^9 N · m^2/C^2
Elemental charge (e) = 1.6 × 10^(-19) C
Distance between electrons (r) = 0.87 cm = 0.87 × 10^(-2) m
Substituting the values into the formula:
Electric force = (9 × 10^9 N · m^2/C^2) * (1.6 × 10^(-19) C)^2 / (0.87 × 10^(-2) m)^2
Simplifying the equation:
Electric force = (9 × 10^9) * (1.6^2 × 10^(-19)^2) / (0.87^2 × 10^(-2)^2) N
Electric force = 2.89 × 10^(-8) N
Therefore, the electric force between these two electrons is approximately 2.89 × 10^(-8) Newtons.
Now, let's move on to calculating the gravitational force between these two electrons.
We can use Newton's Law of Universal Gravitation to calculate the gravitational force between two objects:
Gravitational force = (Gravitational constant * mass1 * mass2) / (distance between electrons)^2
Given:
Gravitational constant (G) = 6.7 × 10^(-11) N · m^2/kg^2
Mass of the electron (m) = 9 × 10^(-31) kg
Substituting the values into the formula:
Gravitational force = (6.7 × 10^(-11) N · m^2/kg^2) * (9 × 10^(-31) kg)^2 / (0.87 × 10^(-2) m)^2
Simplifying the equation:
Gravitational force = (6.7 × 10^(-11)) * (9^2 × 10^(-31)^2) / (0.87^2 × 10^(-2)^2) N
Gravitational force = 7.75 × 10^(-62) N
Therefore, the gravitational force between these two electrons is approximately 7.75 × 10^(-62) Newtons.
Electric force:
ke^2/R^2
1. Use R = 0.0087 meters
k = 9*10^9 N·m^2/C^2
e = 1.6*10^-19 C
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2. Gravitational force:
G*m^2/R^2
G = 6.7×10−^11 N·m^2/kg^2
m = 9.1*10^31 kg
Use same R as abOve