The farther the pickup is from the strings, the weaker the output. It actually drops off at the square of the distance.
This means that when the string is close to the pickup, it stays within an area of magnetic flux that is fairly uniform in density and direction. So string movements are fairly linearly translated into current flow.
However when a string is further away the flux density is higher towards the centre of the magnet, and of course the direction of the flux lines off-center are no longer at right angles to the string's movement. So you're right, we lose efficiency, but not linearly. Large amplitude string vibrations are reproduced less effectively than small amplitude. So pickups maybe sound a little thinner, and obviously have less output. But the thing I really like is that if you hit the strings quite hard, the early part of the note has a little less attack, and as the note dies there is a compressor like effect that enhances the sustain as the string is vibrating close to the magnet centre line. I appreciate the signal will potentially be noisier, but it's not a problem with humbuckers so far.
FWIW I remember telling someone what I liked about the sound of slightly bigger string to pickup clearances before I figured out what it is likely to be caused by (he thought I was mad). Years later as I learnt more about e.m. theory I decided this was a good explanation for what I was hearing.
I tend to run single coil pickups at slightly closer spacing, but then they have such different tonal and note shaping characteristics...
I know none of this is new - but I still think it's valid to do the experiment for yourself - it does more than just weaken the output. And whether the theory works or not, I bought a Les Paul a couple of months back, tried playing it, thought "euch!", and had to back the pickups off to where they sounded good to me. When I think about it I'll measure where the "sweet spot" was for me.
Had enough yet, David? I could type all night (forgot how much I enjoy heated debate on ampage - thank you!)
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