Coulomb's Law | Electrostatics | Electrical engineering | Khan Academy

Summary

This video explains the concept of electric charge, attraction, and repulsion between charged particles. It delves into Coulomb's Law, which predicts the electrostatic force between two charges, and compares it to Newton's law of gravitation. By examining examples and calculations, the video highlights how the force between charges is proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. It concludes with an example calculating the electrostatic force between two charges, demonstrating both the magnitude and direction of the force.

Takeaways

• 🔋 Understanding charge: Same charges repel each other, while different charges attract each other.
• ⚛️ Charge is a property of matter and plays a significant role in electrostatic interactions.
• 📜 Historical context: Electrostatics have been studied for centuries, but it wasn't until the 16th and 17th centuries that serious scientific investigation began.
• 📚 Coulomb's law: Formulated by Coulomb in 1785, it predicts the electrostatic force between two charges.
• 🧲 Coulomb's law formula: The electrostatic force (F) is proportional to the product of the magnitudes of the charges (q1 and q2) and inversely proportional to the square of the distance (r) between them.
• 🌌 Similarity to gravity: Coulomb's law mirrors Newton's law of gravitation, with both forces being inversely proportional to the square of the distance between objects.
• 💡 Electrostatic constant (k): Approximately 9 x 10^9 N·m²/C², used to calculate the magnitude of the electrostatic force.
• 🔢 Example calculation: The video demonstrates calculating the electrostatic force between two charges, 5 x 10^-3 C and -1 x 10^-1 C, separated by 0.5 meters.
• 📐 Force magnitude: Using Coulomb's law and given values, the force is calculated to be 1.8 x 10^7 Newtons.
• 🎯 Direction of force: Since the charges have opposite signs, the force is attractive; if the charges were the same, the force would be repulsive.

Q & A

What is the fundamental principle behind the interaction between two charged objects?

Charged objects with the same sign repel each other, while objects with opposite charges attract each other.

What is Coulomb's Law and why was it significant?

Coulomb's Law, published in 1785, is a formula that predicts the electrostatic force of attraction or repulsion between two charged particles. It was significant because it allowed for the manipulation and prediction of electrostatic forces in a mathematical and scientific manner.

How does Coulomb's Law relate to the magnitude of electrostatic force between two charges?

Coulomb's Law states that the magnitude of the electrostatic force is directly proportional to the absolute value of the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.

What is the mathematical expression for Coulomb's Law?

The mathematical expression for Coulomb's Law is \( F = k \cdot \frac{|q_1 \cdot q_2|}{r^2} \), where \( F \) is the force, \( k \) is the electrostatic constant, \( q_1 \) and \( q_2 \) are the charges, and \( r \) is the distance between the charges.

Why does Coulomb's Law mirror Newton's Law of Gravitation?

Both laws describe a force that is proportional to the product of two quantities (charges or masses) and inversely proportional to the square of the distance between them, showing a similar pattern of interaction at different scales.

What is the difference between the electrostatic force and the gravitational force in terms of strength and range?

The electrostatic force is much stronger at close range and can easily overcome the gravitational force, but the gravitational force is perceived as stronger due to its role in governing the motion of celestial bodies over large distances.

What is the electrostatic constant (k) and its approximate value?

The electrostatic constant (k) is a proportionality constant in Coulomb's Law, and its approximate value is \( 9 \times 10^9 \) Newton meter squared per Coulomb squared.

How can you determine if the force between two charges is attractive or repulsive?

The force is attractive if the charges have opposite signs and repulsive if they have the same sign.

In the example given, what is the charge of the first particle and the distance between the two particles?

The first particle has a positive charge of 5 × 10^-3 Coulombs, and the distance between the two particles is 0.5 meters.

What is the calculated magnitude of the electrostatic force between the two particles in the example, and what is its unit?

The calculated magnitude of the electrostatic force is 1.8 × 10^7 Newtons.

What is the direction of the force between the two particles in the example?

The force is an attractive force because the two particles have charges of opposite signs.

Outlines

00:00

🔋 Understanding Charge Interactions and Coulomb's Law

This paragraph introduces the concept of electric charge and its interactions. It explains that like charges repel and unlike charges attract. The speaker then delves into the historical development of understanding these interactions, known as electrostatics, and highlights the significance of Coulomb's Law published in 1785. Coulomb's Law is presented as a formula to predict the electrostatic force between two charged particles, emphasizing its proportionality to the product of the charges and inverse proportionality to the square of the distance between them. The paragraph also draws a comparison between Coulomb's Law and Newton's Law of Gravitation, noting the similarities in their mathematical forms and the differences in the strength of the forces they describe.

05:00

📚 Applying Coulomb's Law: A Practical Example

The second paragraph provides a practical application of Coulomb's Law with a step-by-step example. The speaker sets up a scenario with two charges of different signs and magnitudes and calculates the electrostatic force between them. The explanation includes the use of the electrostatic constant (k), which is approximated for simplicity. The calculation is detailed, showing the process of determining the magnitude of the force, which is an attractive force due to the opposite charges. The speaker also discusses the units involved in the calculation and how they cancel out to result in Newtons, the unit of force. The final result is presented in scientific notation, illustrating a significant electrostatic force between the two particles.

10:02

🧲 Direction and Magnitude of Electrostatic Force

The final paragraph concludes the discussion by addressing the direction of the electrostatic force, which is attractive in the given example due to the opposite charges of the particles. It reiterates the magnitude of the force calculated in the previous paragraph, emphasizing its significance and the amount of charge involved at the specified distance. The speaker also briefly mentions what would happen if the charges were the same, resulting in a repulsive force instead. This paragraph wraps up the explanation by summarizing the key takeaways about the direction and magnitude of the electrostatic force between charged particles.

Keywords

💡Charge

Charge refers to the property of matter that causes it to experience a force in an electromagnetic field. In the script, charge is central to the discussion of electrostatic forces. It is described as either positive or negative, with like charges repelling and opposite charges attracting each other, as illustrated by the scenario where two objects with the same charge repel and those with different charges attract.

💡Electrostatics

Electrostatics is the branch of physics that deals with electric charges at rest. The script mentions that the study of electrostatics has been observed throughout human history but became more systematic and mathematical in the 16th and 17th centuries. The term is used to describe the study of the forces between charged particles and how they interact.

💡Coulomb's Law

Coulomb's Law is a fundamental principle in electrostatics that quantifies the amount of force between two stationary, electrically charged particles. The script explains that it was formally published by Coulomb in 1785 and is used to predict the electrostatic force of attraction or repulsion between two charges. The law is central to the video's theme of understanding how charged particles interact.

💡Force of Attraction/Repulsion

The force of attraction or repulsion describes the interaction between charged particles. In the script, it is explained that these forces are what cause particles with the same charge to repel and those with opposite charges to attract. The magnitude and direction of these forces are determined by the charges' magnitudes and their distance from each other.

💡Magnitude

In the context of the script, magnitude refers to the size or strength of a force, such as the electrostatic force between two charges. It is used to describe the numerical value of the force without considering its direction, which is crucial in understanding the strength of the interaction between charged particles.

💡Distance

Distance is a key factor in Coulomb's Law, as it determines the strength of the electrostatic force between two charges. The script explains that the force is inversely proportional to the square of the distance between the charges, meaning that as the distance increases, the force decreases rapidly.

💡Proportional

Proportional in the script refers to the relationship between two quantities that change together at a constant rate. Coulomb's Law states that the electrostatic force is proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them, illustrating a direct relationship between charge magnitudes and force.

💡Absolute Value

Absolute value is used in the script to discuss the magnitude of the product of the charges, disregarding whether the charges are positive or negative. This is important because Coulomb's Law is concerned with the strength of the force, not its direction, so the absolute value ensures that the force calculation is always positive.

💡Newton's Law of Gravitation

Newton's Law of Gravitation is mentioned in the script to draw a parallel with Coulomb's Law. It states that the force of gravity between two masses is proportional to the product of their masses and inversely proportional to the square of the distance between them. The script uses this law to highlight the similarity in the mathematical relationship between gravitational and electrostatic forces.

💡Electrostatic Constant

The electrostatic constant, denoted as 'K' in the script, is a proportionality constant in Coulomb's Law that relates the magnitude of the electrostatic force to the product of the charges and the square of the distance between them. The script approximates this constant for the sake of simplicity in the example calculation, emphasizing its importance in quantifying electrostatic forces.

💡Scientific Notation

Scientific notation is a way of expressing very large or very small numbers and is used in the script to simplify the presentation of the calculated electrostatic force. The script converts the calculated force into scientific notation to make it easier to understand and communicate the magnitude of the force.

Highlights

Introduction to the concept of charge and its interaction, where like charges repel and opposite charges attract.

Historical context of electrostatics and the formal publication of Coulomb's law in 1785.

Coulomb's law's purpose is to predict the electrostatic force of attraction or repulsion between two charged particles.

Explanation of the variables in Coulomb's law, including charges (q1 and q2) and the distance (r) between them.

Coulomb's empirical discovery that the electrostatic force is proportional to the product of the charges and inversely proportional to the square of the distance.

Comparison of Coulomb's law to Newton's law of gravitation, highlighting the similarity in their mathematical forms.

The difference in the strength of gravitational and electrostatic forces and their relevance at different scales.

Application of Coulomb's law with an example involving charges of 5 * 10^-3 C and -1 * 10^-1 C separated by 0.5 meters.

Introduction of the electrostatic constant (k) and its role in calculating the electrostatic force.

Calculation of the electrostatic force using the given values and the electrostatic constant, resulting in a significant force of 1.8 * 10^7 Newtons.

Discussion on the direction of the force, indicating attraction between particles of opposite charges and repulsion between like charges.

The significance of the calculated electrostatic force in understanding the interactions at the atomic level.

The importance of Coulomb's law in the study of physics, particularly in the fields of electrostatics and electromagnetism.

The practical implications of understanding electrostatic forces, such as in the design of electronic devices and materials.

Encouragement for the audience to engage with the material by pausing the video and applying the formula to understand the concept deeply.

Transcripts

- [Voiceover] So we've already started to

familiarize ourselves with the notion of charge.

We've seen that if two things have the same charge,

so they're either both positive,

or they are both negative,

then they are going to repel each other.

So in either of these cases

these things are going to repel each other.

But if they have different charges,

they are going to attract each other.

So if I have a positive and I have a negative

they are going to attract each other.

This charge is a property of matter

that we've started to observe.

We've started to observe of how these different charges,

this framework that we've created,

how these things start to interact with each other.

So these things are going to,

these two things are going to attract each other.

But the question is, what causes,

how can we predict how strong the force

of attraction or repulsion is going to be

between charged particles?

And this was a question people have noticed,

I guess what you could call electrostatics,

for a large swathe of recorded human history.

But it wasn't until the 16 hundreds

and especially the 17 hundreds,

that people started to seriously view this

as something that they could manipulate

and even start to predict in a kind of serious,

mathematical, scientific way.

And it wasn't until 1785, and there were many

that came before Coulomb,

but in 1785 Coulomb formally published

what is known as Coulomb's law.

And the purpose of Coulomb's law,

Coulomb's law,

is to predict what is going to be the force of

the electrostatic force of attraction or repulsion

between two forces.

And so in Coulomb's law, what it states is

is if I have two charges,

so let me, let's say this charge right over here,

and I'm gonna make it in white,

because it could be positive or negative,

but I'll just make it q one, it has some charge.

And then I have in Coulombs.

and then another charge q two right over here.

Another charge, q two.

And then I have the distance between them being r.

So the distance between these two charges

is going to be r.

Coulomb's law states that the force,

that the magnitude of the force,

so it could be a repulsive force

or it could be an attractive force,

which would tell us the direction of the force

between the two charges,

but the magnitude of the force,

which I'll just write it as F,

the magnitude of the electrostatic force,

I'll write this sub e here,

this subscript e for electrostatic.

Coulomb stated, well this is going to be,

and he tested this, he didn't just kind of guess this.

People actually were assuming that it had something

to do with the products of the magnitude

of the charges and that as the particles

got further and further away

the electrostatic force dissipated.

But he was able to actually measure this

and feel really good about stating this law.

Saying that the magnitude of the electrostatic force

is proportional,

is proportional,

to the product of the magnitudes of the charges.

So I could write this as q one times q two,

and I could take the absolute value of each,

which is the same thing as just

taking the absolute value of the product.

Here's why I'm taking the absolute value of the product,

well, if they're different charges,

this will be a negative number,

but we just want the overall magnitude of the force.

So we could take, it's proportional to

the absolute value of the product of the charges

and it's inversely proportional to

not just the distance between them,

not just to r, but to the square of the distance.

The square of the distance between them.

And what's pretty neat about this

is how close it mirrors Newton's law of gravitation.

Newton's law of gravitation, we know that the force,

due to gravity between two masses,

remember mass is just another property of matter,

that we sometimes feel is a little bit more tangible

because it feels like we can kind of see weight and volume,

but that's not quite the same,

or we feel like we can feel or

internalize things like weight and volume

which are related to mass,

but in some ways it is just another property,

another property, especially as you get into more

of a kind of fancy physics.

Our everyday notion of even mass starts to

become a lot more interesting.

But Newton's law of gravitation says,

look the magnitude of the force of gravity

between two masses is going to be proportional to,

by Newton's, by the gravitational concept,

proportional to the product of the two masses.

Actually, let me do it in those same colors

so you can see the relationship.

It's going to be proportional to

the product of the two masses, m one m two.

And it's going to be inversely proportional

to the square of the distance.

The square of the distance between two masses.

Now these proportional personality constants

are very different. Gravitational force,

we kind of perceive this is as acting, being strong,

it's a weaker force in close range.

But we kind of imagine it as kind of what dictates

what happens in the,

amongst the stars and the planets and moons.

While the electrostatic force at close range

is a much stronger force.

It can overcome the gravitational force very easily.

But it's what we consider happening

at either an atomic level or kind of at a scale

that we are more familiar to operating at.

But needless to say, it is very interesting

to see how this parallel between these two things,

it's kind of these patterns in the universe.

But with that said, let's actually apply

let's actually apply Coulomb's law,

just to make sure we feel comfortable with the mathematics.

So let's say that I have a charge here.

Let's say that I have a charge here,

and it has a positive charge of, I don't know,

let's say it is positive five

times 10 to the negative three Coulombs.

So that's this one right over here.

That's its charge.

And let's say I have this other charge right over here

and this has a negative charge.

And it is going to be,

it is going to be, let's say it's negative one...

Negative one times 10

to the negative one Coulombs.

And let's say that the distance between the two,

let's that this distance right here

is 0.5 meters.

So given that, let's figure out what the

what the electrostatic force

between these two are going to be.

And we can already predict that

it's going to be an attractive force because

they have different signs.

And that was actually part of Coulomb's law.

This is the magnitude of the force,

if these have different signs, it's attractive,

if they have the same sign then they

are going to repel each other.

And I know what you're saying,

"Well in order to actually calculate it,

"I need to know what K is."

What is this electrostatic constant?

What is this electrostatic constant going to actually be?

And so you can measure that with a lot of precision,

and we have kind of modern numbers on it,

but the electrostatic constant,

especially for the sake of this problem,

I mean if we were to get really precise it's 8.987551,

we could keep gone on and on times 10 to the ninth.

But for the sake of our little example here,

where we really only have

one significant digit for each of these.

Let's just get an approximation,

it'll make the math a little bit easier,

I won't have to get a calculator out,

let's just say it's approximately

nine times 10 to the ninth.

Nine times 10 to the ninth.

Nine times, actually let me make sure it says approximately,

because I am approximating here,

nine times 10 to the ninth.

And what are the units going to be?

Well in the numerator here,

where I multiply Coulombs times Coulombs,

I'm going to get Coulombs squared.

This right over here is going to give me,

that's gonna give me Coulombs squared.

And this down over here is going

to give me meters squared.

This is going to give me meters squared.

And what I want is to get rid of

the Coulombs and the meters and end up

with just the Newtons.

And so the units here are actually,

the units here are Newtons.

Newton and then meters squared,

and that cancels out with the meters squared

in the denominator.

Newton meter squared over Coulomb squared.

Over, over Coulomb squared.

Let me do that in white.

Over, over Coulomb squared.

So, these meter squared will cancel those.

Those Coulomb squared in the denomin...

over here will cancel with those,

and you'll be just left with Newtons.

But let's actually do that.

Let's apply it to this example.

I encourage you to pause the video

and apply this information to Coulomb's law

and figure out what the electrostatic force

between these two particles is going to be.

So I'm assuming you've had your go at it.

So it is going to be, and this is really

just applying the formula.

It's going to be nine times 10 to the ninth,

nine times 10 to the ninth,

and I'll write the units here,

Newtons meter squared over Coulomb squared.

And then q one times q two, so this is going to be,

let's see, this is going to be,

actually let me just write it all out for this first

this first time.

So it's going to be times five times ten

to the negative three Coulombs.

Times, times negative one.

Time ten to the negative one Coulombs

and we're going to take the absolute value of this

so that negative is going to go away.

All of that over, all of that over

and we're in kind of the home stretch right over here,

0.5 meters squared.

0.5 meters squared.

And so, let's just do a little bit of the math here.

So first of all, let's look at the units.

So we have Coulomb squared here,

then we're going to have Coulombs times Coulombs there

that's Coulombs squared divided by Coulombs squared

that's going to cancel with that and that.

You have meters squared here,

and actually let me just write it out,

so the numerator, in the numerator,

we are going to have

so if we just say nine times five

times, when we take the absolute value,

it's just going to be one.

So nine times five is going to be,

nine times five times negative...

five times negative one is negative five,

but the absolute value there,

so it's just going to be five times nine.

So it's going to be 45

times 10 to the nine,

minus three, minus one.

So six five,

so that's going to be 10 to the fifth,

10 to the fifth, the Coulombs already cancelled out,

and we're going to have Newton meter squared over,

over 0.25

meters squared. These cancel.

And so we are left with,

well if you divide by 0.25,

that's the same thing as dividing by 1/4,

which is the same thing as multiplying by four.

So if you multiply this times four,

45 times four is 160

plus 20 is equal to 180

times 10 to the fifth Newtons.

And if we wanted to write it in scientific notation,

well we could divide this by,

we could divide this by 100 and then multiply this by 100

and so you could write this as 1.80

times one point...

and actually I don't wanna make it look like

I have more significant digits than I really have.

1.8 times

10 to the seventh,

times 10 to the seventh units,

I just divided this by 100 and I multiplied this by 100.

And we're done.

This is the magnitude of the electrostatic force

between those two particles.

And it looks like it's fairly significant,

and this is actually a good amount,

and that's because this is actually a good amount of charge,

a lot of charge.

Especially at this distance right over here.

And the next thing we have to think about,

well if we want not just the magnitude,

we also want the direction,

well, they're different charges.

So this is going to be an attractive force.

This is going to be an attractive force on each of them

acting at 1.8 times ten to the seventh Newtons.

If they were the same charge, it would be a repulsive force,

or they would repel each other with this force.

But we're done.