What Are the Uses and Effects of Fields in Physics and Mathematics?

[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!