The Nobel laureate Richard Feynman once said that if two...

The Nobel laureate Richard Feynman 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.

Key Concepts

Electric Charge and Charge Imbalance

Electric charge is a fundamental property of matter determined by the presence of protons and electrons. Under normal conditions, matter is electrically neutral because the positive and negative charges balance each other. However, even a slight imbalance, where there is a small excess of one type of charge, can lead to a measurable net charge. Understanding this principle is crucial in analyzing how minute discrepancies at the microscopic level can produce significant macroscopic electrical effects.

Electrostatic Force and Coulomb's Law

Coulomb's law describes the force between two point charges, stating that the magnitude of the electrostatic force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This concept emphasizes that even small net charges can result in large forces if either the magnitude of the charges is significant or if the objects are close to each other. It is a key concept in estimating the repulsive force between objects with an imbalance in charge.

Order-of-Magnitude Estimation

Order-of-magnitude estimation is a technique used to approximate values to the nearest power of ten, enabling simplifications in complex calculations without requiring precise data. This approach is particularly useful in physics to gauge whether a phenomenon, such as an electrostatic force, is strong enough to have noticeable effects, such as overcoming gravitational forces. It helps in developing a conceptual understanding of the scales involved in physical interactions.

Gravitational Force Comparison

Gravitational force is the attractive force between masses, fundamental in determining the weight of an object. Comparing the gravitational force to the repulsive electrostatic force requires an estimation of both forces and an understanding of how they scale relative to each other. This comparison is essential for evaluating claims about the magnitude of one force relative to another, especially when a small charge imbalance could theoretically produce a force that rivals or exceeds gravitational attraction on a large scale.

Transcript

00:01 So in this problem, we need to show that if two persons and they're separated by the distance of one arm, which is on average 0 .5 meters, if one person had just 1 % more electrons than protons, compared to another person that can be assumed to be neutral, then the force of repulsion will be so strong that it will be equal to the gravitational force of the earth fg.

00:31 So first we see how many protons there are in human body.

00:39 And knowing that human body mostly consists of the water molecules, we can assume that whole body of a human being is like a body of water, and the number of protons is we should divide the other, some average weight of a protein.

01:06 Person, which is, for example, 80 kilograms, we should divide that by the molar mass of the water and then multiply that by molecules per mole number and then multiply that by protons per molecule number.

01:23 And in this case, water has 10 protons per molecules.

01:29 So we can write 80 kilograms over 0 .018 kilograms per moles.

01:40 So this is the molar mass of the water times the number which states how many molecules are there per one mole on the water times 10 protons per molecule.

02:15 And this equals to 2 .68 times 10 to 28 protons.

02:21 So the charge is then, this is the positive charge in this case number of protons times e or the fundamental charge.

02:37 This equals to the 10 to the negative 19 columns which is equal to 4 .29 times 10 to the 9 power columns.

03:09 So this, this here, this quantity of charge, then we need to find what is 1 % of this.

03:22 So this would be quantity of charge if we had a completely charged person...

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