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Let's say that you have a bullet going through the metal screen. Into screen. It makes a dot-like hole, like here:

enter image description here

Now, let's say that we have a bullet going out of screen. It makes a jagged, sharp edges, often 3-4 of them, making it often look like an X, just like here:

enter image description here enter image description here

It doesn't necessarily have to be a bullet. It can be a nail, a dart, a compass needle point or many other everyday items, going through different materials with the similar effect as above, making this result something very intuitive.

However, in physics, mostly electromagnetism, we are presented with completely opposite denomination, i.e. dot meaning out of screen and X meaning into screen, which is reverse of the intuitive logic above:

enter image description here enter image description here

What is the reason behind it? Is it because of some tradition or historical reasons? I studied math (and some physics, though I quit on 4th semester) for quite several years and never understood it, and it was counter-intuitive for me. Even more for some people I know that always had a problem with this symbolism.

I memorized it myself by using the very fact of it being reversed (for me, in my personal opinion), as to never mistake it, which is kinda funny, to always have to think of opposite!

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    $\begingroup$ I always made sense of it by thinking of a common dart: the front is pointy, while the back has four flaps to stabilize it. $\endgroup$ Jan 8, 2023 at 10:12
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    $\begingroup$ It's supposed to be like an arrow. When it's coming towards you the dot represents the point and when it's going away from you the cross represents the fletching. $\endgroup$ Jan 8, 2023 at 10:19
  • $\begingroup$ @JacopoTissino if you think about the dart/arrow, doesn't it go down to the same logic I wrote above? You throw the dart into the screen and it hits it with the pointy tip, so it's a dot. And if the dart is thrown at you from the screen, out of screen, then the point of contact with the screen is the four flaps to stabilize it. Because it's the screen, the cross section of the space that we are analyzing, that's the most important thing here, right? It's the frame of reference that we should use, why would I think about myself instead of the screen? That is what I find counterintuitive! :) $\endgroup$
    – Kusavil
    Jan 8, 2023 at 10:25
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    $\begingroup$ What's intuitive/natural and what's not for you is not really debatable, but the idea (that's probably intuitive to most people) is that you're looking at the screen with a dart/arrow crossing it (or in front of it), and you draw the first thing you see. The leap to drawing from the perspective of the screen is not really intuitive to me. $\endgroup$ Jan 8, 2023 at 10:34
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    $\begingroup$ I say, "Forget the screen." Think about a dart on a very foggy day. If it's coming towards you, you just see the pointy end. If it's going away from you, you just see the tail 'feathers'. $\endgroup$ Jan 8, 2023 at 11:00

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You just need to have the right picture in mind, then it's actually very intuitive and easy to remember. From rfcafe.com:

arrows

We anyway draw fields as arrows. Now, imagine someone shot an arrow in the plane and it got stuck, so you either see the pointy end just barely sticking out or the fletching (the feather cross at the tail end).

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  • $\begingroup$ It might be worth emphasizing that we normally draw fields (or vectors in general) with arrows showing direction, so this is the natural way to think about it. $\endgroup$ Jan 9, 2023 at 1:31
  • $\begingroup$ Thanks @DavidBailey, done. $\endgroup$
    – rfl
    Jan 9, 2023 at 11:58

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