Two electrons are separated by 1 meter. What is the ratio of the magnitude of the electric force on one electron and the gravitational force on that electron due to the other electron? The charge of an electron is 1.6×10−19C and its mass is 9.1×10−31kg.
To find the ratio of the magnitude of the electric force to the gravitational force between two electrons, we can use the formulas for electric force and gravitational force.
1. Calculate the electric force between the two electrons:
The electric force between two charges can be found using Coulomb's Law:
F_electric = k * (q1 * q2) / r^2
Where:
F_electric is the electric force
k is Coulomb's constant (k = 8.99 × 10^9 N m^2/C^2)
q1 and q2 are the charges of the electrons (q1 = q2 = 1.6 × 10^-19 C)
r is the distance between the charges (r = 1m)
Plugging in the values:
F_electric = (8.99 × 10^9 N m^2/C^2) * ((1.6 × 10^-19 C) * (1.6 × 10^-19 C)) / (1m)^2
2. Calculate the gravitational force between the two electrons:
The gravitational force between two masses can be found using Newton's Law of Universal Gravitation:
F_gravitational = G * (m1 * m2) / r^2
Where:
F_gravitational is the gravitational force
G is the gravitational constant (G = 6.67430 × 10^-11 m^3 kg^-1 s^-2)
m1 and m2 are the masses of the electrons (m1 = m2 = 9.1 × 10^-31 kg)
r is the distance between the masses (r = 1m)
Plugging in the values:
F_gravitational = (6.67430 × 10^-11 m^3 kg^-1 s^-2) * ((9.1 × 10^-31 kg) * (9.1 × 10^-31 kg)) / (1m)^2
3. Calculate the ratio:
To find the ratio, divide the electric force by the gravitational force:
Ratio = F_electric / F_gravitational
Now you can plug in the values and solve for the ratio.