What is a Field? I Don't Understand

[joshi-wan kenobi]

I know it's a basic question, but I don't understand this one either. And I can't find an answer anywhere. I've seen the iron filings and the magnetic field lines with my own eyes but what is it? What makes it curve like that and come back around? What's it made of?

 

[mathman]

Rough definition:

At each point in space (near the magnet) the force exerted on magnetically affected stuff (iron filings) has a strength and direction. This (vector) function of position is called a (vector) field. The concept of field is much more general, but this gives you some idea.

 

[chroot]

A field is the assignment of some mathematical object to each point in a space.

The field \phi = 0 simply assigns the scalar 0 to every point. You can refer to the field as \phi. This field is called, appropriately, a scalar field. A real world example of a scalar field is the temperature in your room. At each point in the room's volume, there is a specific scalar assigned: the temperature.

The field \phi = 2 \mathbf{k} assigns the vector 2 \mathbf{k} to each point in space. If you consider the \mathbf{i} - \mathbf{j} plane, every point in the plane is assigned a vector that sticks perpendicularly out of the plane. This field is called, appropriately, a vector field. A real world example is, as mathman showed, the electric or magnetic field. At each point in space, there is a vector representing the strength and direction of the field.

- Warren

 

[chroot]

Originally posted by joshi-wan kenobi
What makes it curve like that and come back around? What's it made of?

The reason the iron filings line up is because they interact with the field.

Consider again a vector field, which assigns to each point in space a vector. If you imagine drawing a curve through this field of vectors, such that the vectors at each point along the curve are tangent to the curve, you have what is known as a "field line."

When a filing is perpendicular to the field lines, it feels a torque which tends to rotate it. When it is parallel with the field lines, it feels no more torque. Thus, all the iron filings line up along the field lines, and you can see what direction the field is pointing.

The strength of the field is related to the number of lines in a given volume. The more tightly packed the lines of force, the stronger the field. Thus, the field is strongest near the poles of the magnet, where all the filings tend to congregate. At the poles, all of the field lines are coming together and going into the magnet body, to re-emerge on the other side.

- Warren

 

[joshi-wan kenobi]

Those are all good explanations but what are lines of force? What is this force made of? Photons?

 

[lethe]

a field is really a rule that assigns an object to each point in spacetime, like chroot said.

think of a stream, with water flowing down it. you can point your finger anywhere in the stream, and see which way the water is flowing, and how fast. that means that every point in the stream has a vector assigned to it, which tells the direction and speed of the water at that point.

now think of a large charged object. anywhere i point my finger near this charged object, i can put another charged object, and there will be a force pushing the new object.

this is an electric force field. every point in space around my charged object gets assigned a vector that describes the force. how big the force is, and what direction its pointing in, depends on which point in space i choose

and that s about it.

lines of force are just lines that you trace out that follows the force field vectors at each point.

and forget about photons. the field isn t made of anything. its just a bookkeeping device.

 

[joshi-wan kenobi]

I hope you'll excuse me if I'm a little slow on this one. :) But I still don't understand.

When you put your finger or the charged object into the stream, aren't you tapping into an energy source that's already there, the stream? I'm guessing this is the battery or power source? Then if that's true, does that make the stream a wire connecting two terminals and the force you feel, the field around the wire?

And if the field isn't made of anything, how does it exert a force?

 

[lethe]

Originally posted by joshi-wan kenobi

And if the field isn't made of anything, how does it exert a force?

there are two ways of looking at how one object exerts a force on another: action at a distance, or a local field.

action at a distance means that if i put two objects next to each other, then their gravitational attractions just pull on each other from across the empty space between them.

Newton introduced this idea, but he didn t like it, and most others don't either.

instead, we prefer to describe how things exert forces on each other with force fields. i put one object in the room, and there is a force field around it. put the other object in the room as well, and it feels the part of the field that it is sitting on top of.

the two descriptions are equivalent (at least in the static case). so its just a choice of preference. you can either choose to say object A exerts 10 Newtons on object B, or you can say, object A has a force field where the force at point P is 10 Newtons, and object B happens to be at point P.

either way, the answer is the same: object B feels a force of 10 Newtons.

 

[cucumber]

what about force-carrier particles??

is there not some sort of particle transmitted between for eg two magnets or something?

something like gravitons for magnets (if gravitons do exist...)

what would be the force-carrier particle for charged objects?

and how do these force-carrier particles work anyway? how can a north and a south pole of a magnet "know" that the other is there and be pulled towards it??
does my head in.

 

[lethe]

Originally posted by cucumber
what about force-carrier particles??

yes, in quantum field theory, the field is mediated by vector bosons, and if you want me to talk about those, i can, but i think that for the purposes of this thread, where we are trying to understand what a field is on the classical level, it is only going to obscure the discussion.

 

[jimmy p]

All i ever thought of as a field was an area around an object where another particle would experience a force. Simple but effective i think.

 

[lethe]

Originally posted by jimmy p
Simple but effective i think.

i agree. that sounds about right to me.

 

[joshi-wan kenobi]

Yeah, I get that there's a field around an object and that the field diminshes over distance and that other objects feel the force and that there's field lines. But all of that is the effect, not the cause. What I don't understand is what the field is made of and how it works. I figure it's got to be made of something, right? It's there afterall, doing work. I know it can't be magic. Is there a book I can read about this that describes how magnets work and not just what they do?

 

[jimmy p]

As someone said earlier, no one actually KNOWS why they work, they just do. There are books saying how they work, just look in any decent textbook, but i suppose you would have to look for theories and theses as the why they work.