Nobel laureate Richard Feynman (1918-1988) once said that if...

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-ofmagnitude calculation to substantiate this assertion.

Key Concepts

Coulomb's Law

Coulomb's Law describes the electrostatic force between two charged objects. It states that the force is proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This fundamental law is key for understanding how small imbalances in electrical charge can lead to significant forces between objects.

Electrostatic Forces

Electrostatic forces arise from interactions between charged particles. Even a tiny net charge on macroscopic bodies can lead to large forces if the conditions align, as described by Coulomb's Law. This concept is important for understanding how slight deviations from electrical neutrality can create forces capable of overcoming gravitational forces.

Order-of-Magnitude Estimation

Order-of-magnitude estimation is a technique used to approximate a value within a factor of ten. This approach is useful in physics to quickly gauge the scale of a phenomenon without requiring precise calculations, allowing for the assessment of whether theoretical predictions, such as those involving nearly neutral objects generating enormous forces, are reasonable.

Charge Imbalance in Matter

The concept of charge imbalance in matter refers to the slight excess of electrons or protons that can occur even in predominantly neutral atoms. This imbalance, although very small on an atomic scale, can accumulate over a large number of atoms, leading to significant macroscopic effects such as the generation of strong electrostatic forces.

Transcript

00:01 Okay, here's a fun problem.

00:03 We let two people stand across from each other for a very simple picture.

00:13 An arm's length from each other.

00:15 I'm going to go ahead and say that an arm's length means one meter.

00:20 We're going to assume each of them has the same mass, and i'm going to let that mass for a person be, well, we're talking a simple calculation here.

00:31 So let's make it nice round numbers wherever we can.

00:35 100 kilograms.

00:39 Now, if each of these people had 1 % more electrons than protons.

00:48 So in other words, the number of electrons is equal to 1 .01, the number of electrons is equal to 1 .01, the number of protons.

01:10 Well, how many is that? well, i can get the number of protons approximately from the mass of my person, right? because we are mostly protons.

01:23 Protons and neutrons.

01:25 It's not going to, hang on.

01:27 That might confuse things.

01:30 So instead, let's make a simple chemistry assumption and say, my body is primarily made out of water.

01:41 H2o.

01:42 Oxygen has eight protons, and hydrogen each has one proton.

01:51 So we add another two.

01:53 So that gets us 10 protons per oxygen molecule.

02:02 I can get, or per water molecule.

02:05 I can get the weight of water and get the number of water molecules that make up my body and therefore number of protons that make up my body.

02:16 So let's do some quick googling.

02:20 I find the mass of a water molecule at about three times 10 to the minus 26 kilograms, which means.

02:38 Means the number of water molecules in my body is going to be 100 divided by this is about 33 times 10 to the 28 molecules...

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