Are lines of force measurable?

[YADA]

Does the strength of a magnetic field become weaker at a constant rate the further you get away from it? I ask this question for two reasons.

1 - When iron filings are placed on a piece of paper and and a magnet is placed under it, there are definite lines of magnetic force visible that become less obvious the further they are away from the magnet.

2 - When I was into electronics, I built a crystal radio and attached a single transistor amplifier to it. I then removed the tuning coil and replaced it with a single piece of wire and replaced the tuning capacitor with one of a fixed value (I can't remember what value). I noticed that as my hand moved close to the circuit a tone was generated in the ear piece that changed in a non-linear fashion. There would be a tone, then silence, a different tone, then more silence as my hand moved closer or further from the circuit. It also worked with electrical wiring behind a wall, whether or not the wire was part of an active circuit.

So, are the lines of force you see in diagrams of magnetic fields actual, measurable, lines of force with 'gaps' of lesser strength between them? What about gravitational fields and electromagnetic fields?

I've tried researching it on the net, but I'm definitely not up with the technical aspects!

 

[mikelepore]

Any kind of field, electric, magnetic or gravitational, would fall off linearly with distance only if you had a geometry where it falls off in the same way the circumference of a circle increases with radius. Therefore, if you consider the magnetic field generated by a long, straight current-carrying wire, you have cylindrical symmetry in the magnetic field around it, so expect the expression for magnetic field at some point in space to have a (2 pi r) in the denominator. For magnets of irregular shape, the relationship may or may not be approximately linear, but never perfectly linear.

 

[gutti]

Take a look at the inverse square law, that may help.

 

[mikelepore]

There are no real gaps between the lines on a diagram. The symbolism is that the lines being closer together, that is, drawing more lines per unit of area on the diagram, represents the field having a greater magnitude. Therefore lines are close together at the poles of a magnet, and further apart at some distance away.

The historical curiosity is that Michael Faraday was poor at mathematics, so he invented diagrams with lines to represent electrical and magnetic fields without having to describe them with equations. Maxwell later have Faraday's discoveries mathematical expression.

 

[Dale]

Fields are measurable, and they do decay in a characteristic "dipole" fashion. The field lines are just a graphing tool, useful for plotting a field on a piece of paper.

 

[YADA]

Thanks very much for the responses. I read about the Inverse Square Law and Maxwell's 'update' of Faraday. So the magnetic field just gets weaker the further it gets from the magnet.

What about my point two? The tone generated wasn't a tone that went from weak to strong or high pitched to low pitched in one go. I noticed that at a certain dstance from my skin, it would give a certain tone, at other distances there would be no tone. The tones were repeatable for the distances; ie. at 15 cm there would be a certain tone. If I moved it away and then back to 15 cm, I would get the same tone. The same thing occurred with the electrical wire.

Any ideas on what was being measured or picked up?