cp Strength of the Electric Force. Imagine two 1.0 -g bags of protons, one at the earth's north

Cp Strength of the Electric Force. Imagine two 1.0 -g bags...

Key Concepts

Force Comparison and Magnitude Estimation

Comparing the magnitudes of different forces, such as electric repulsion versus gravitational attraction, highlights the vast differences in strength between fundamental forces. Estimating these forces and understanding their relative sizes is important in fields ranging from electrostatics to astrophysics, allowing for the assessment of when certain forces become significant or negligible in a given context.

Scaling from Microscopic to Macroscopic Quantities

This concept involves transitioning from the properties of individual particles, such as the mass and charge of a single proton, to a macroscopic assembly of many particles. By scaling these microscopic quantities, one can calculate aggregate properties such as total mass, overall charge, and the resulting interactions between large collections of particles.

Elementary Charge

The elementary charge is the fundamental unit of electric charge, typically represented by the charge of a proton or electron. Understanding the magnitude of the elementary charge is crucial when calculating the total charge of a collection of particles and applying Coulomb’s Law to determine the force between charged bodies.

Newton’s Law of Gravitation

Newton’s Law of Gravitation explains the attractive force between two masses. According to the law, every mass exerts an attractive force on every other mass, and the strength of this gravitational attraction is proportional to the product of the masses and inversely proportional to the square of the distance between their centers. This law is essential for analyzing how large masses interact under the influence of gravity.

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 two charges and inversely proportional to the square of the distance between them. This principle is fundamental in understanding how charges (such as protons) interact, whether they attract or repel one another.

Transcript

00:01 In this exercise, we have two bags of protons, one placed at the north pole and one place at the south pole on earth.

00:10 And those two bags have equal mass.

00:14 They all have one gram of protons.

00:18 And exercise a asks us to calculate what is the number of protons we have in each bag.

00:30 So we can simply calculate this by using a rule of three.

00:37 So i'll write here in the first column number of protons, and here mass.

00:50 And we know that the mass of one proton is a well -known quantity, is 1 .67 times 10 to the minus 27, and we want to know how many protons, sorry, we want to know how many protons and we have, in one gram, we can simply multiply 1 times 10 to the minus 3 by 1 and multiply our variable n by the mass of one proton.

01:39 In the end, what you find is that n is equal to 1 times 10 to the minus 3 over 1 .67 times 10 to the minus 27.

01:58 And this is equal to 6 times 10 to the 23.

02:07 So this means that a bag that contains one gram of protons has six times 10 to the 23 protons in it.

02:20 And this is the answer of our first exercise.

02:26 Question b asks us to calculate what is the gravitational force fg and the electric force f .e that one bag exerts on the other one.

02:40 So what is the gravitational force, for instance, that the back at the north pole exerts on the back on the south pole, and what is the electric force of the back, or the north pole exerts on the back on the south pole.

02:55 So starting with the gravitational force, we have that expression for the gravitational force is the gravitational constant g that are the value here, times the mass of the body that generates the gravitational field, which in this case is the mass of one bag, m, times the mass of the body that feels the gravitational field, which is also m, over the distance between the two bodies squared.

03:30 And in this case, it's the distance between the north pole and the south pole, which is two times the radius of earth.

03:40 So it's two are squared.

03:45 If we substitute these values here, we have that fg is equal to 6 .67 times 10 to minus 11 times 1 times 10 to the minus 3 squared over 2 times 6 .6 .38.

04:21 Times 10 to the 6 squared.

04:27 And we find that the gravitational force generated by one bag of protons and felt by the other bag of protons is 4 .1 times 10 to the minus 31 newtons.

04:44 It's a very, very weak force.

04:50 Now that we are done with this, we are left with the electric force to calculate.

04:55 And if we remember the expression for the electric force is equal to the charge of the body that is under the electric fields, that we'll call key total, times the electric fields.

05:18 Key total is the total charge of one bag of protons...

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