Nobel laureate Richard Feynman (1918-1988) once said that if two persons stood at arm's length from each other and each person had 1% more electrons than protons, the force of repulsion between them would be enough to lift a "weight" equal to that of the entire Earth. Carry out an order-of-magnitude calculation to substantiate this assertion.

F ~ 10 N

http://www.physics.drexel.edu/~wking/courses/phys102_s08/notes/rec1_sols.pdf

To substantiate Feynman's assertion, we can perform an order-of-magnitude calculation using Coulomb's law to calculate the force of repulsion between two charged objects. Coulomb's law states that the force between two point charges is proportional to the product of their charges and inversely proportional to the square of the distance between them.

Let's assume each person has a mass of about 70 kg (average human weight) and their "weight" is equal to m*g, where g is the acceleration due to gravity.

Step 1: Calculate the mass of the Earth
The mass of the Earth is approximately 5.97 x 10^24 kg.

Step 2: Calculate the number of electrons and protons in each person
The average number of electrons and protons in an atom is the same, which is around 10^23.

Step 3: Calculate the charge of each person
Since each person has 1% more electrons than protons, the net charge on each person can be calculated as:
Charge = (1% / 100) * Number of electrons = (1/100) * 10^23 = 10^21 C

Step 4: Calculate the distance between the two people
Let's assume they are standing at arm's length, which is approximately 1 meter.

Step 5: Calculate the force of repulsion between the two people
Using Coulomb's law:
F = (k * q1 * q2) / r^2

where k is the electrostatic constant, approximately 9 x 10^9 N m^2/C^2, q1 and q2 are the charges on the two people, and r is the distance between them.

F = (9 x 10^9 N m^2/C^2) * (10^21 C) * (10^21 C) / (1 m)^2
F = 9 x 10^51 N

Since the force is directly proportional to the masses, the result of this force is much larger than the gravitational force on both people. Therefore, the force of repulsion would indeed be enough to lift a "weight" equal to that of the entire Earth, as Richard Feynman stated.

To substantiate Richard Feynman's assertion about the force of repulsion between two people with an excess of electrons, we can carry out an order-of-magnitude calculation.

First, let's determine the weight of the Earth. The weight of an object is given by the formula W = mg, where m is the mass and g is the acceleration due to gravity. The mass of the Earth is approximately 5.972 × 10^24 kilograms, and the acceleration due to gravity is approximately 9.81 meters per second squared. Therefore, the weight of the Earth would be:

W = (5.972 × 10^24 kg) × (9.81 m/s^2)
W ≈ 5.86 × 10^25 N

Now, let's calculate the force of repulsion between two people. The force between two charged objects can be calculated using Coulomb's law, which states that the force is proportional to the product of the charges and inversely proportional to the square of the distance between them.

Let's assume that each person has 1% more electrons than protons. Electrons and protons have the same magnitude of charge but opposite signs (+1.6 × 10^-19 Coulombs for each). So, if each person has an extra 1% of the electrons, the charge on each person can be approximated as:

q = (1% × 1.6 × 10^-19 C) = (0.01 × 1.6 × 10^-19 C) = 1.6 × 10^-21 C

To calculate the force of repulsion, we need to estimate the distance between the two people standing at arm's length. Let's assume that it is approximately 1 meter (m).

Using Coulomb's law, the force of repulsion (F) between the two people can be calculated as:

F = k * (q^2 / r^2)

where k is the electrostatic constant (approximately 8.99 × 10^9 N m^2/C^2), q is the charge on each person, and r is the distance between them.

F = (8.99 × 10^9 N m^2/C^2) * [(1.6 × 10^-21 C)^2 / (1 m)^2]
F ≈ 3.27 × 10^-11 N

Comparing this calculated force to the weight of the Earth, we see that the force of repulsion is significantly smaller than the weight of the Earth (3.27 × 10^-11 N vs. 5.86 × 10^25 N). Therefore, the assertion made by Richard Feynman is not substantiated by this order-of-magnitude calculation.