What Is the Difference Between Electric Potential Energy and Electric Potential? | Physics in Motion

Summary

This segment of 'Physics in Motion' explores the concept of electric potential energy, the energy stored by electric charges. It explains how this energy can be converted into electrical power for various applications. The script delves into the factors affecting electric potential energy, including charge type, amount, and electric field strength, and demonstrates calculations using Coulomb's Law. It also distinguishes between electric potential energy and electric potential, highlighting their roles in our daily use of electricity. The video concludes with the importance of understanding these concepts for harnessing electric power.

Takeaways

• 💧 Gravitational potential energy is stored energy in water that can be converted to kinetic energy for hydroelectric power.
• 🔋 Electric potential energy is the energy stored by electric charges, which can be used to generate electrical energy.
• 🛠 Electrical engineers need to understand electric potential energy for designing circuits that power various devices.
• 📏 Electric potential energy is a scalar quantity that can be positive or negative, indicating energy loss or gain in a system.
• ⚡ The electric potential energy depends on the type of charge, the amount of charge, and the strength of the electric field.
• 🔢 The formula for electric potential energy is given by \( k \times \frac{q_1 \times q_2}{r} \), where \( k \) is Coulomb's constant, and \( q_1, q_2 \) are the charges.
• 🔌 Electric potential energy and electric potential are measured in Joules and volts, respectively, with volts being Joules per Coulomb.
• 🔄 Electric potential energy is conservative, following the law of conservation of energy, converting between potential and kinetic energy.
• 🔃 The electric potential at a point is the sum of the potentials due to individual charges at that point.
• 📐 The electric potential energy equation can be compared to the gravitational potential energy equation, with mass replaced by charge and height by distance within the field.
• 🔌 Electric potential, or voltage, is the electric potential energy per unit charge and is a key concept in understanding and harnessing electric power.

Q & A

What is gravitational potential energy?

Gravitational potential energy is the stored energy that can be converted into kinetic energy by the force of gravity. It is the energy an object possesses due to its position in a gravitational field.

How can gravitational potential energy be converted into hydroelectric power?

Gravitational potential energy can be converted into hydroelectric power when the potential energy of water (due to its height) is released and used to turn turbines, which then generate electricity.

What is electric potential energy?

Electric potential energy is the energy stored by electric charges, which can be converted into electrical energy to do work, such as powering devices and running electrical circuits.

Why is it important for electrical engineers to know the amount of electric potential energy in their circuits?

Knowing the amount of electric potential energy is essential for electrical engineers to design circuits that can provide the necessary power for various applications, from small devices to large-scale systems.

What is the formula for calculating electric potential energy between two point charges?

The formula for calculating electric potential energy (U) between two point charges is U = k * (q1 * q2) / r, where k is Coulomb's constant, q1 and q2 are the charges, and r is the distance between them.

What does the negative sign in the calculated electric potential energy indicate?

A negative electric potential energy indicates that work must be done on the system to keep the charges apart, reflecting the potential for the charges to do work if they are allowed to move closer together.

How does the electric potential energy change as a charge moves within an electric field?

As a charge moves within an electric field, its electric potential energy changes based on its position relative to other charges. If it moves against the electric field, its potential energy increases; if it moves with the field, its potential energy decreases, often converting to kinetic energy.

What is the relationship between electric potential energy and the conservation of energy?

Electric potential energy is a conservative force, meaning it obeys the law of conservation of energy. The energy lost in potential form is gained in kinetic form and vice versa, ensuring the total energy in a closed system remains constant.

How is electric potential energy similar to gravitational potential energy?

Both electric and gravitational potential energy depend on the position of an object within a field and can be either positive or negative. They both have the potential to do work based on their position and can be converted into other forms of energy.

What is electric potential, and how is it different from electric potential energy?

Electric potential, also known as voltage, is the electric potential energy per unit charge. It is different from electric potential energy in that the latter refers to the total energy stored in a system of charges, while the former refers to the energy per single unit of charge.

How do you calculate the electric potential at a point due to multiple charges?

To calculate the electric potential at a point due to multiple charges, you sum the potentials at that point due to each individual charge. The total electric potential at a point is the scalar sum of the potentials from all contributing charges.

What units are used to measure electric potential energy and electric potential?

Electric potential energy is measured in Joules, while electric potential, or voltage, is measured in volts, which is equivalent to Joules per coulomb.

Outlines

00:00

🌊 Gravitational and Electric Potential Energy Explained

This paragraph introduces the concept of gravitational potential energy, which is the energy stored in water due to gravity's pull, and its conversion to kinetic energy for hydroelectric power. It then transitions to electric potential energy, the energy stored by electric charges, and its importance in electrical engineering for powering various devices. The paragraph explains that electric potential energy is a scalar quantity that can be positive or negative and depends on the type of charge, the amount of charge, and the electric field's strength. It also provides a formula and example calculation for determining electric potential energy, emphasizing the role of electric charges and fields in this process.

05:00

🔋 Understanding Electric Potential and Its Conservation

The second paragraph delves deeper into electric potential energy, comparing it to gravitational potential energy and highlighting its conservative nature, adhering to the law of conservation of energy. It describes scenarios affecting electric potential energy, such as the positioning of charges and the direction of movement in an electric field. The paragraph introduces the concept of electric potential, or voltage, as the electric potential energy per unit charge and differentiates it from electric potential energy. It also presents the equation for electric potential energy between two charged plates and relates it to the equation for gravitational potential energy, simplifying the understanding of electric potential in terms of volts.

10:02

🔌 Calculating Electric Potential with Multiple Charges

The final paragraph focuses on calculating electric potential in situations involving multiple charges. It provides a step-by-step example of how to determine the total electric potential at a point influenced by two charges, explaining the process of adding scalar quantities. The example given involves calculating the potential at a specific point due to two charges with different magnitudes and signs, and at different distances from the point. The paragraph concludes by emphasizing the importance of understanding electric potential and energy for harnessing everyday electrical power, and it invites viewers to explore further with the 'Physics in Motion' toolkit.

Keywords

💡Gravitational Potential Energy

Gravitational potential energy is the energy stored in an object due to its position in a gravitational field. In the video, it is introduced as the energy stored in water that can be converted to kinetic energy and then to hydroelectric power. The concept is central to understanding how energy can be harnessed from natural forces, as seen in the example of water in a dam that can be used to generate electricity.

💡Kinetic Energy

Kinetic energy is the energy an object possesses due to its motion. The script explains that when gravitational potential energy is converted into kinetic energy, it can power various applications like heating homes and running computers. The term is crucial for understanding the transformation of energy from one form to another, which is a key theme in the video.

💡Electric Potential Energy

Electric potential energy is the energy stored by electric charges, which can be converted into electrical energy. The video discusses this concept as a foundational principle in electrical engineering, essential for designing circuits that power various devices. It is a central concept in the video, illustrating the storage and conversion of energy in electrical systems.

💡Electric Field

An electric field is a region around a charged particle where an electric force is exerted on other charged particles. The script uses the electric field as a key element in explaining how electric potential energy is generated and how it can perform work. The electric field is depicted as a force that influences the potential energy of charges within it.

💡Scalar Quantity

A scalar quantity is a physical quantity that can be described by a magnitude alone, without direction. In the video, electric potential energy is described as a scalar, which means it only has size and not direction, unlike vector quantities. This distinction is important for understanding how energy is measured and calculated in physics.

💡Charge

Charge is a fundamental property of matter that causes it to experience a force when placed in an electromagnetic field. The video script emphasizes the role of charge in determining electric potential energy, as it is a key factor in the amount of energy that can be stored and the work that can be done by an electric field.

💡Conservation of Energy

The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. The video explains that electric potential energy is conservative, meaning it obeys this law, and whatever energy is lost as potential energy is gained as kinetic energy, and vice versa, which is a central theme in understanding energy transformations.

💡Electric Potential

Electric potential, also known as voltage, is the electric potential energy per unit charge. The video distinguishes between electric potential energy and electric potential, explaining that the latter is a measure of energy for a single unit of charge. This concept is vital for understanding how electrical energy is quantified and utilized in everyday applications.

💡Coulomb's Constant

Coulomb's constant is a fundamental physical constant that appears in the formula for the electric force between two point charges. In the script, it is used in the calculation of electric potential energy and potential, showing its importance in quantifying the interactions between charges and their fields.

💡Work

In physics, work is done when a force causes or tends to cause movement of an object in the direction of the force. The video script uses the concept of work to explain how electric potential energy can be converted into kinetic energy, and vice versa, when a charge moves within an electric field, illustrating the practical application of energy transformations.

💡Voltage

Voltage, or electric potential difference, is the amount of energy required to move a unit charge from one point to another. The video script uses the term voltage to connect the concept of electric potential to everyday electrical systems, emphasizing its role in the distribution and use of electrical energy.

Highlights

Gravitational potential energy is the stored energy in water that can be converted into kinetic energy for hydroelectric power.

Electric potential energy is the energy stored by electric charges and can be used to generate electrical energy.

Electric potential energy is essential for designing circuits that power everything from toothbrushes to stadium lights.

Electric potential energy is the work performed on a charged object by an electric field and is a scalar quantity.

Electric potential energy can be positive or negative, indicating energy loss or gain in a system.

The electric potential energy formula involves the constant k, charges, and the distance between them.

A calculation example demonstrates how to find the electric potential energy of a point charge in an electric field.

The negative result of electric potential energy signifies the work needed to keep charges apart.

Electric potential energy decreases and converts into kinetic energy as a charge moves in an electric field.

Electric potential energy is conservative, obeying the law of conservation of energy.

The electric potential energy of a charge near another positive charge is high, while near a negative charge, it is low.

Electric potential energy is analogous to gravitational potential energy, both depending on an object's position in a field.

The equation for electric potential energy between two charged plates is derived by comparing it to gravitational potential energy.

Electric potential, or voltage, is the electric potential energy per unit charge and is measured in volts.

Electric potential at a point in space is determined by the amount of charge and the distance from it.

The total electric potential at a point is the sum of the potentials from multiple charges.

A practical example shows how to calculate the total electric potential at a point due to multiple charges.

Understanding electric potential energy and potential is key to harnessing everyday electrical power.

Transcripts

♪♪

(Anzar) Look at all that water.

Just think about the energy that is stored in there,

ready to do work.

That form of energy is called gravitational potential energy,

stored energy that gravity can turn into kinetic energy.

When it does become kinetic energy,

it can be converted to hydroelectric power

that can heat homes, restaurants and stores,

and run computers.

But gravity isn't the only force that can have potential energy.

In this segment, we're going to talk about

electric potential energy.

That's energy stored by electric charges.

When we know the amount of electric potential energy

we can store,

we also know the amount of electrical energy

we can generate.

When electrical engineers designed the circuits

that provide electrical power,

they need to know how much electric potential energy

they have to work with.

And that's essential for running everything

from electric toothbrushes

to lights in football stadiums.

Let's dig a little deeper into electric potential energy.

We know that it's the magnitude of the work

performed on a charged object

by an electric field.

In other words, electric potential energy

is the energy that a charge in an electric field possesses

which gives it the ability to do work.

Like all forms of energy,

electric potential energy is a scalar quantity,

but unlike other scale or quantities

like speed and temperature,

it can be positive or negative.

Now, it has nothing to do with direction,

like it would in a vector quantity,

but is determined by whether energy

is lost or gained in a system.

Electric potential energy depends on three things.

The type of charge,

whether it's positive or negative,

the amount of charge,

and the strength of the electric field it's in.

Electric potential energy uses the same units

as gravitational potential energy, Joules.

We can figure out how much energy a system has

by considering the electric charges

and fields that are involved.

Let's do a quick calculation to see how that works.

Say you have a charge of positive five

times ten to the negative twelve coulombs,

creating an electric field.

If a second point charge of negative three times

ten to the negative 15 coulombs is seven meters away,

what is the electric potential energy

stored by the second charge?

Electric potential energy equals a constant k

times a product of the charges

divided by the distance between them.

Now we plug in what we know.

K is nine times ten to the ninth

Newton meters squared per coulomb squared.

This is multiplied by the first charge,

positive five times ten to the negative twelve coulombs

times the second charge,

which is negative three times ten

to the negative fifteenth coulombs

divided by a distance of seven meters.

Plugging these values into the electric potential energy

equation gives us negative 1.9

times ten to the negative seventeen Newton meters.

Since a Newton meter equals one Joule,

our answer is that the electric potential energy

of the second point charge

equals negative 1.9

times ten to the negative 17 Joules.

Notice that the sine of each charge matters

and the answer is a negative number.

The negative sign tells us that work must be done

on the system to keep these charges apart,

so electric potential energy is the ability of a charge

to do work.

But how does that, well, work?

Let's say we have two charged plates.

The top plate is positively charged,

and the bottom plate is negatively charged.

You can see the electric field lines

going from the positive plate to the negative plate.

Let's put a positive charge

in the electric field.

Work must be done to push a positive charge

towards a positive plate

or away from the negative plate.

When the positive charge is moving

opposite the direction of the electric field,

we call that moving up the field.

the further up the field the positive charge goes,

the more work you have to do.

Like, if you were pushing a ball uphill.

When the positive charge is here,

near the positive plate,

what kind of electric potential energy

does it possess?

If you said it's high or strong,

that's right.

In fact, we can say that the charge

has maximum electric potential energy.

The charge doesn't want to be up here.

So if you let it start to move,

it will be repelled away

from the positive plate,

and attracted towards the negative plate.

It will accelerate all the way down.

While it's falling, what's happening?

Think back to gravitational potential energy

of the dam, because this works

in a very similar way.

If your answer was that the electric potential energy

is decreasing,

being converted into kinetic energy,

you're right.

When it reaches the negative plate

at maximum velocity,

how much electric potential energy is left?

If you said none, you got it right again.

It has no electric potential energy left.

It all changed to kinetic energy.

Another important characteristic

of electric potential energy

is that it is conservative.

Which means that it obeys the law of conservation of energy.

Whatever an object loses in potential energy

it gains in kinetic energy,

and vice versa.

Now let's look at what happens to electric potential energy

in different scenarios.

A positive charge near another positive charge

has high potential energy.

A positive charge near a negative charge

has low potential energy.

A positive charge gains electric potential energy

when it is moved in a direction

opposite the electric field.

A negative charge gains electric potential energy

when it is moved in the same direction

as the electric field.

Those are the basics of electric potential energy,

which has a strong resemblance

to gravitational potential energy.

Both depend on the position of an object in a field,

and both can be positive or negative.

To understand the equation for electric potential energy

stored by a charge between two charged plates,

let's look at the equation for gravitational potential energy

and compare it to electric potential energy.

The potential energy of an object

due to gravity equals its mass

times gravitational field strength

times its height.

So, the electrical equivalent of mass

is charge, which is q,

where g represents

the strength of the gravitational field,

we replace it with electric field, e.

And the height above ground becomes the distance

above the bottom plate.

So we can write the equation for electric potential energy

stored by a charge between two charged plates

as the charge q,

times the electric field e,

times the distance the charge has moved

within the field, d.

We've seen what electric potential energy is,

and that it is equal to the work

a charge in a field can do,

but how can we talk about it

in a way that makes it useful to us.

One way to describe it is per unit charge,

which we call electric potential.

Be careful not to confuse the two.

I know the names are similar,

but when we have a system with many charges,

electric potential energy

tells us the energy of all the charges

we're working with.

Electric potential tells us the energy of a single unit

of charge.

Electric potential, represented by a v,

is the electric potential energy per unit charge.

Let's talk about units,

and that will make the difference between

electric potential energy

and electric potential easier to understand.

Energy is measured in units of Joules, right?

A volt is defined as a Joule per coulomb.

When we calculate electric potential,

we can simplify the units to volts.

Electric potential is also called voltage.

This term connects electric potential

to the electricity we harness everyday.

Electric potential at a point in space

depends on two main factors;

the amount of charge creating the potential,

and the distance from that charge.

We can write this out as another type of equation

that looks like this.

Electric potential, v,

equals Coulomb's Constant, k,

times a charge responsible for the potential, q,

divided by the distance, r,

from q.

What if we want to solve for electric potential

at a point at which potential

is created by more than one charge.

The electric potential of multiple charges equals

the sum of the potential of each individual charge

at a point in space.

Like electric potential energy,

electric potential is a scalar quantity,

so it's easy to add together.

Now, how does that work?

Say we have two charges; q sub 1,

and q sub 2,

and a point in space we'll call point A.

Q sub 1 is one meter from point A,

and q sub 2 is three meters from point A.

Q sub 1's charge is negative five times ten

to the negative six coulombs,

and q sub 2's is positive five

times ten to the negative six coulombs.

We want to know what is the electric potential

at point A.

Recall that electric potential V

equals k times q,

divided by r.

The potential at point A from q sub 1

equals k times q sub 1

divided by the distance between q sub 1

and point A.

K equals nine times ten to the ninth

Newton meters squared per coulomb squared.

Q sub 1 equals negative five time ten

to the negative sixth coulombs,

and r equals one meter.

Plugging these numbers into the equation,

we find that the potential at point A

due to q sub 1

equals negative 45,000 Newton meters

per coulomb, or volts.

There's still one more thing that effects the potential

at point A, and that's q sub 2.

The electric potential at point A

equals the potential at point A

due to q sub 1, plus the potential

at point A due to q sub 2.

So to solve for the total potential at point A,

we'll need to know the potential at A

from q sub 2 as well.

The potential at point A from q sub 2

equals k times q sub 2

divided by the distance between them.

Q sub 2 is positive five times ten

to the negative six coulombs,

and the distance, r, is three meters.

Plugging these numbers into the equation,

we see that the potential at point A

from q sub 2 equals 15,000 volts.

That means the total potential at point A

is negative 45,000 volts,

plus 15,000 volts,

which equals negative 30,000 volts.

That's the total electric potential at point A

due to q sub 1 and q sub 2.

Now, I know we've covered a lot here,

but these are key concepts for you to understand

energy contained in electric charges

and how we measure it.

We went over two terms with similar names.

Electric potential energy,

or energy stored by electric charges,

and electric potential,

which is the measure of electric potential energy

per single unit of charge.

We can use both to help harness the electric power

that we use everyday.

That's it for this segment of "Physics in Motion,"

and we'll see you next time.

(announcer) For more practice problems,

lab activities and note-taking guides,

check out the "Physics in Motion" toolkit.