Understanding the Difference Between V=kq/d and W=qEd in Electric Potential

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In summary, the two equations discussed are not the same and are used in different contexts. V represents electric potential, while W represents work or energy. The formula V=k\frac{q}{d} is used for calculating potential at a distance d for point charges, while the formula W=qEd is used for calculating the work needed to move a charge in an electrical field. The general formula is W=qV, but for a uniform electrical field, V=Ed and W=qEd can be used.
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Procrastinate
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I'm really confused about these two equations; are they the same or do they denote different things?

I know they are both to do with electric potential, but in what context do I employ them in? Our teacher told us to use one of them in a uniform field and another one of them in a non-uniform field but I don't remember which one is which.

Thanks in advance.
 
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  • #2
No, V is the electric potential (not potential energy) and W is work (energy). The electrical potential energy, not to be confused with the electric potential, is the potential energy a charge has in an electrical field.

It is similar to gravity, where if you lift an object a short distance h from the ground the object has a potential energy of mgh. The work required to lift that object a distance h is then also mgh. The electric field works the same way. When you move an object away from an electrical charge you have to do work.

The formula [itex]V=k\frac{q}{d}[/itex] gives the potential at a distance d. This formula is only valid for point charges. The formula [itex]W=qEd[/itex] is the work needed to move a charge q in an electrical field E a distance d. The general formula is W=qV, for a uniform electrical field V=Ed. Therefore you can only use W=qEd for a point charge in a uniform electrical field.
 
  • #3


Both V=kq/d and W=qEd are equations used to calculate electric potential, but they represent different concepts. V=kq/d is used to calculate the electric potential at a specific point in a uniform electric field, where k is a constant, q is the charge creating the field, and d is the distance from the charge. This equation is used when the electric field is constant in magnitude and direction.

On the other hand, W=qEd is used to calculate the work done by an electric field on a charge as it moves between two points. Here, W represents work, q is the charge, E is the electric field, and d is the distance traveled. This equation is used in non-uniform electric fields, where the electric field may vary in magnitude and direction.

It is important to understand the difference between these equations and when to use them. In a uniform electric field, V=kq/d can be used to calculate the potential at any point, whereas W=qEd is used to calculate the work done by the field on a charge. In a non-uniform field, W=qEd can be used to calculate the work done on a charge as it moves between two points, taking into account the varying electric field. Using the wrong equation in the wrong context can lead to incorrect results.

I would recommend consulting your textbook or teacher for more clarification on when to use each equation and practicing with different examples to solidify your understanding. Understanding these equations and their applications is crucial in the study of electric potential and its effects on charges.
 

1. What does the equation V=kq/d or W=qEd represent?

The equation V=kq/d or W=qEd represents the relationship between electric potential (V), electric force (F), and the distance between two charges (d). It is also known as Coulomb's Law.

2. How is the value of k determined in the equation V=kq/d or W=qEd?

The value of k is a constant known as the Coulomb's constant, which is equal to 8.99 x 10^9 Nm^2/C^2. It is determined experimentally and is used in the equation to calculate the electric force between two charges.

3. Is the equation V=kq/d or W=qEd applicable to all types of charges?

Yes, the equation V=kq/d or W=qEd is applicable to all types of charges, whether they are positive or negative. The only difference is that the force between two charges with the same sign will be repulsive, while the force between two opposite charges will be attractive.

4. Can the equation V=kq/d or W=qEd be used for point charges only?

No, the equation V=kq/d or W=qEd can also be used for extended charges, as long as the distance between them is measured from the center of each charge. It can also be used for continuous charge distributions, by integrating the equation.

5. What are the units of the variables in the equation V=kq/d or W=qEd?

The units of electric potential (V) are volts (V), the units of electric force (F) are newtons (N), and the units of distance (d) are meters (m). The units of the constant k are Nm^2/C^2, while the units of charge (q) are coulombs (C). Therefore, the units of the entire equation are volts (V).

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