Exploring the Nature of Fields: Their Uses & Effects

[jwxie]

Homework Statement

Here is an interesting reading to my question.
http://coraifeartaigh.wordpress.com/2010/02/27/what-is-a-field/

The author wrote:

It is clear from Coulomb’s law above that the force experienced by any charge B due to A will also depend on the magnitude of B i.e. each charge you bring up to A will experience a different force!

The reason he said each charge will experience a different force is assuming different r (and not a constant r)?

Another question is to understand the purpose of a field (in mathematics and physics).

So a field is use to describe the effect of a test particle that places in space?

Any help is appreciated! Thank you.

 

[Uku]

The test particle will experience a force which depends on the distance from the point-charge and on it's own charge magnitude.

"Each charge you bring up to A will experience a different force" is valid if the charges are different in magnitude.

There is no "purpose" for a field. It just exists. Rather, a test particle is used to describe the field.

 

[collinsmark]

Hello jwxie,

Homework Statement

Here is an interesting reading to my question.
http://coraifeartaigh.wordpress.com/2010/02/27/what-is-a-field/

The author wrote:The reason he said each charge will experience a different force is assuming different r (and not a constant r)?

I admire your desired to learn the meaning behind the equations! But I don't think the author was talking about different 'r' values. Instead, I think the author was talking about different q values, where q is the electric charge of B. In other words, if we only talk about forces and forces alone, the force on (B) caused by charge (A) is

$$F = k \frac{q_A q_B}{r^2}$$

So when the author says, "force experienced by any charge B due to A will also depend on the magnitude of B" I think he's talking about different values of q_B.

Another question is to understand the purpose of a field (in mathematics and physics).

So a field is use to describe the effect of a test particle that places in space?

Well, I think the author is trying to say that the purpose of defining a field in the first place is to determine the effects that charge (A) has on the space around it, while removing the dependency of q_B.

While it's an otherwise well written article, I think it might be a little unclear on this point. Let's call charge (B) the test charge. Then the magnitude of the electric field caused by charge (A) is

$$E = F/q_B = \frac{k\frac{q_A q_B}{r^2}}{q_B} = k\frac{q_A}{r^2}.$$

Notice the magnitude of the electric field caused by (A) is not a function of the charge of test charge q_B, which can be anything. I think that is what the author is trying to say.

[Edit: 'Looks like Uku beat me to the point.]

 

[jwxie]

Ha, Great helps from both of you. Appreciated.

I am not so bright when it comes to understanding the math and physics concepts. It takes me quite a while to understand every thing. Well that's how an ordinary physics major is. I wished I was a genius in math and physics LOL.

Thank you!

 

[rwisz]

I find this reading on the nature of fields to be quite interesting. The author brings up an important point that the force experienced by a charge will vary depending on its distance from another charge. This is due to Coulomb's law, which states that the force between two charges is inversely proportional to the square of the distance between them. Therefore, as the distance between the charges changes, so does the force.

To answer the question about the purpose of a field, we must first understand what a field is. In physics, a field is a physical quantity that has a value at every point in space. Examples of fields include electric fields, gravitational fields, and magnetic fields. These fields can be described mathematically using equations, allowing us to understand and predict their effects on particles in space.

In this context, the purpose of a field is to describe the effect that a test particle would experience if placed in that field. For example, if we have a test charge placed in an electric field, the field will exert a force on the charge, causing it to move. By understanding the properties of the field, we can predict how the test charge will behave.

I hope this helps to clarify the concept of fields and their uses in physics and mathematics. It is a fundamental concept in many areas of science, and further exploration and understanding of fields can lead to new discoveries and advancements in our understanding of the natural world.