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In my text book magnetic flux density is defined as the number of field line per units of area. what I know is the field line is just a conceptual imagination , which doesn't really exist, but then how can we "count" the number of field lines to know how much flux density is there?

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  • $\begingroup$ Maybe relevant Here $\endgroup$ – Buraian Nov 11 '20 at 10:37
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It's true that you can't actually see the magnetic field lines but what you can see or demonstrate is their effects. Let me give you an analogous example. Say you have two different sources of light, one is smaller than the other. So we usually use this kind of description that "First Source is Brighter Than the second one and therefore, the First Source is emitting more rays of light than the second one", when in reality, nobody can actually see a ray of light (if you are finding this hard to believe, look at a source of light nearby and try counting the rays of light coming from it...!) so you can't count the rays of light because you can't see them. What you can still do is observe or measure their effects. Similar argument can be used to justify your doubts about magnetic field lines. We can't see the magnetic field lines but what we see are there effects and by comparing their effects, we can compare their strength(in this case magnetic flux density) and therefore one property of magnetic field lines state that," the magnetic field lines are crowded in a region where the field is stronger and they are widely spaced in region where the field is weaker". What it actually means is that: First you do all the measurements and verifications about the strength of the field and then you can comment about the number of magnetic field lines in that region or over that area. So even if you can't see a magnetic field line (or a Ray of light) you still can measure or predict the magnitude of the field strength over a certain space or an area.

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