how far apatr should two electrons be if the electric force each exerts on the other is equal to the weight of an electron ? ( take the mass of an electron to be Me = 9.11 x 10-31 kg ).
To find the distance between two electrons such that the electric force they exert on each other is equal to the weight of an electron, we need to equate the two forces and solve for the distance. Let's break it down step by step:
1. The electric force between two charged objects is given by Coulomb's law:
F = k * (q1 * q2) / r^2
where F is the electric force, k is the electrostatic constant (k ≈ 9 x 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between them.
2. In this case, each electron exerts an electric force on the other. Since electrons have a charge of -1.6 x 10^-19 C (coulombs), we can rewrite the equation as:
F = k * ((-1.6 x 10^-19 C) * (-1.6 x 10^-19 C)) / r^2
F = k * (2.56 x 10^-38 C^2) / r^2
3. The weight of an object is given by the equation:
weight = mass * acceleration due to gravity
Since we want the electric force to be equal to the weight of an electron, we can set up the following equation:
F = m * g
where F is the force, m is the mass, and g is the acceleration due to gravity (approximately 9.8 m/s^2).
4. From the problem statement, we are given the mass of an electron (Me = 9.11 x 10^-31 kg). Substituting the values, we have:
m * g = 9.11 x 10^-31 kg * 9.8 m/s^2
F = 8.94 x 10^-30 N
5. Now, we can equate the two forces and solve for the distance (r):
k * (2.56 x 10^-38 C^2) / r^2 = 8.94 x 10^-30 N
6. Rearranging the equation, we have:
r^2 = k * (2.56 x 10^-38 C^2) / (8.94 x 10^-30 N)
r^2 = 2.88 x 10^-9 m^2
7. Taking the square root of both sides to solve for r, we get:
r = √(2.88 x 10^-9 m^2)
r ≈ 1.7 x 10^-5 m
Therefore, the two electrons should be approximately 1.7 x 10^-5 meters (or 17 micrometers) apart for the electric force they exert on each other to be equal to the weight of an electron.
Use F=ma to find the weight of an electron, use a=9.8 m/s^2
use coulombs law
F=k(Q1Q2)/r^2
rearrange to
r^2=k(Q1Q2)/F
use k=8.99 x 10^9 N m^2/C^2
and Q1=Q2=1.60x10^-19 C