# Point charges and electric potential

• fawk3s
In summary, the equation Wp = q * E * r represents the electrical potential energy of a point charge in an electric field. It is derived from the work done by the force acting on the charged particle. This equation can be used for both homogeneous electric fields and point charges, but for point charges, it becomes more complex and requires the use of calculus to account for the changing electric field.
fawk3s
I have some difficulties grasping the idea of this equation

Wp = q * E * r

Where
Wp - electrical potential energy
q - charge
E - the strength of the electric field
r - radius, or distance from the other point charge

So basically, say we have 2 point charges. One positive, and one negative, so they attract.
But I can't imagine how the work done by the moving point charge is the same we get by calculating by that formula. Because the closer the point charge gets to the other point charge, the bigger the E gets. So the electric force applied on that point charge isn't constant. Its getting bigger.
My physics textbook also says that the way to calculate the work done by the point charge in this situation is too difficult to describe in a high school textbook. But yet they still give me that equation. Why?

I can imagine the same thing with Earth and its gravitational potential energy, but the change in g (9,81 m/s2) is so small over short distances that there's no point to really observe it.

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fawk3s said:
I have some difficulties grasping the idea of this equation

Wp = q * E * r

Where
Wp - electrical potential energy
q - charge
E - the strength of the electric field
r - radius, or distance from the other point charge

Im going to assume you know calculus ( if not, integration is the continuous summing of a variable)

The potential energy is the same as the work done to bring the particle to that point from an infinite distance ( ie a distance where the potential energy is 0 )

The electric field E is the force acting on 1 C of charge (sign sensitive ) so q*E gives the force acting on the charged particle.

The work done by this force is given by the intergral of F.dr ( the component of the force in the direction of displacement times the displacement )

Now the equation q*E*r is the case in which F ( ie the electric field E ) is constant over the distance r ( which can be approximately true in some cases though not for point charges )

then the integral becomes F*r = q*E*r

To obtain the work done for 2 point charges we have to integrate E and r which will get complicated as you apply the by-parts integration ( both E and r are functions of r )

hope this helps

Yes, I understand how the equation works in a homogeneous electric field, and they actually gave us Wp = q * E * d for a homogeneous electric field in the textbook, but Wp = q * E * r for point charges. I don't quite understand what to do with the latter since I have no idea how to use it with a changing E. They are basically the same though.

thats what calculus is for.
if you want to do physics then you MUST learn calculus.

conceptually you break the changing field into infinitesimal unchanging parts.
Calculate the energy in each part.
Then add them all up (integrate them)

the integral of an inverse square law will give you an inverse first power law
therefore the energy of an infinitesimal charge falling from infinity
into a finite (unmoving) charge will be proportional to 1/d
where d is the distance from the finite charge.

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I understand your confusion and am here to help clarify the concept of point charges and electric potential. Let's break down the equation Wp = q * E * r to better understand it.

First, Wp represents the electrical potential energy, which is the energy that a charged particle possesses due to its position in an electric field. This energy is measured in joules (J).

Next, q represents the charge of the particle. This can be a positive or negative value, depending on the type of charge the particle has. The unit of charge is coulombs (C).

E represents the strength of the electric field, which is a measure of the force per unit charge exerted on a charged particle. This is measured in newtons per coulomb (N/C).

Finally, r represents the distance between the two point charges. This is measured in meters (m).

So, the equation is essentially telling us that the electrical potential energy (Wp) is equal to the product of the charge (q), the strength of the electric field (E), and the distance between the charges (r). This equation helps us calculate the amount of energy a charged particle has in a given electric field.

Now, let's address your question about the work done by the moving point charge. As the point charge moves closer to the other point charge, the electric field strength (E) does indeed increase. This means that the force acting on the moving charge also increases. However, the equation Wp = q * E * r takes into account this change in force. As the force increases, the distance between the charges (r) decreases, resulting in a balanced equation. This means that the work done by the moving charge remains the same, regardless of the change in force.

As for your textbook's statement about the difficulty in calculating the work done by a point charge in this situation, it is true that the mathematical calculation can be complex. However, the equation Wp = q * E * r is a simplified version that still gives us a good estimate of the work done.

In summary, the equation Wp = q * E * r helps us understand the relationship between electrical potential energy, charge, electric field strength, and distance. It is a simplified version that still gives us valuable information about the energy possessed by a charged particle in an electric field. I hope this explanation helped clarify the concept for you.

## What is a point charge?

A point charge is a hypothetical concept used in physics to represent a charged particle with a non-zero charge but with negligible size. This means that all of the charge is concentrated at a single point in space.

## What is electric potential?

Electric potential is the amount of electrical potential energy that a unit charge would have at a specific point in space, relative to a reference point. It is measured in volts (V).

## How are point charges related to electric potential?

Point charges create electric potential fields around them based on their charge and distance from other charges. These electric potential fields can be calculated using Coulomb's law, which relates the magnitude of the charge to the electric potential at a given point.

## What is the difference between electric potential and electric potential energy?

Electric potential is a measure of the potential energy per unit charge, while electric potential energy is the total potential energy of a system of charges. In other words, electric potential is a property of a point in space, while electric potential energy is a property of a system of points in space.

## How can electric potential be calculated for a system of point charges?

The electric potential at a point in space due to a system of point charges can be calculated by summing the electric potentials of each individual charge. This can be done using the equation V = kQ/r, where V is the electric potential, k is a constant, Q is the charge, and r is the distance from the charge to the point in question.

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