What If We Were Not Neutral? A 75 -kg person holds out his...

What If We Were Not Neutral? A 75 -kg person holds out his arms so that his hands are 1.7 $\mathrm{m}$ apart. Typically, a person's hand makes up about 1.0$\%$ of his or her body weight. For round numbers, we shall assume that all the weight of each hand is due to the calcium in the bones, and we shall treat the hands as point charges. One mole of Ca contains $40.18 \mathrm{g},$ and each atom has 20 protons and 20 electrons. Suppose that only 1.0$\%$ of the positive charges in each hand were unbalanced by negative charge. (a) How many Ca atoms does each hand contain? (b) How many coulombs of unbalanced charge does each hand contain? (c) What force would the person's arms have to exert on his hands to prevent them from flying off? Does it seem likely that his arms are capable of exerting such a force?

Key Concepts

Coulomb’s Law

Coulomb’s Law describes the electrostatic force between two point charges. It states that the magnitude of the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance separating them. The law is fundamental in understanding interactions between charged particles and is widely used to calculate forces in systems where the distance between charges is significant compared to their sizes.

Electric Charge Imbalance

Electric charge imbalance involves situations where there is a difference between the number of positive and negative charges, leading to a net charge. This concept is important for calculating the resultant force in systems where not all charges are balanced, and even a small imbalance can produce measurable electrical effects. Understanding the proportion of charge imbalance is crucial for assessing forces in systems that are nearly neutral but have slight deviations.

Mole Concept

The mole concept is a fundamental chemical counting unit that relates the microscopic scale to macroscopic amounts. It allows chemists and physicists to relate the mass of a substance to the number of particles it contains using Avogadro’s number. This concept is essential in calculating quantities like the number of atoms or molecules in a given mass of material, and it bridges the gap between atomic theory and measurable quantities.

Point Charge Approximation

The point charge approximation treats objects as if all their electrical charge is concentrated at a single point, which greatly simplifies the analysis of forces and fields, especially in electrostatics. This concept is particularly useful when the spatial dimensions of the charged objects are small relative to the distance between them, allowing for simpler calculations of interactions while still providing reliable insights into the system's behavior.

Transcript

00:01 Okay, so we know the mass of the hand is 1 % of body weight, which is 0 .01m.

00:06 M is the body weights.

00:08 So therefore, the number of the calcium addens on the hand should be equal to the mole of the calcium atoms times the abogadros number.

00:19 So we know the mode of the calcium atoms can be equal to the mass of the hand over the molar mass of the calcium atoms, okay? which is 0 .01m over capital m.

00:29 And we know avogadro's number is na.

00:32 So we know mass, for the body mass, which is the body weights of the person's, in this case, is 75 kilograms, which is 75 times 10 to power 3 grams.

00:44 And we know the motor mass of the calcium atoms is 40 .18 gram per mole.

00:49 And we know avogadro's number is 6 .02 times 10 to power 23.

00:54 So now we can determine the number of the calcium addants on each hand, which is equal to, so n is equal to 0 .01 times 75 times 10 to power 3 grams over 40 .1 a gram per mole, and then times 6 .02 times 10 to the power of 23.

01:28 And this will give us the number of calcium atoms in each hand is about 1 .12 times 10 to the power of 25.

01:41 Okay.

01:44 So for the next question, in order to determine the charge on each hand, while we know the charge queue, you know, let's use the lower case queue, okay? so charge q should be equal to 1 % times 20 n and n times e.

02:03 Why is that? because in the question it was saying that only 1 % of the positive charge in each hand will unbalanced by the negative charge, okay? so which means that there are only 1 % of charge on our hands, okay? and we know in each calcium atoms, there are 20 protons and 20 electrons.

02:23 Okay, protons is positive charge, electrons is negative charge.

02:27 Okay, so we can just simply multiply the total number of calcium atoms on our hand by 20.

02:34 So we just pick either proton or electrons to start with.

02:38 So let's pick the protons, okay, because the value will be positive, since it's a positive charge.

02:44 And remember, if we try to determine the charge, the total charge on our hand, we need to multiply by the individual charge of each proton, okay, which is e here...

Please give Ace some feedback