i'm retarded can you understand the maxwell equations intuitively

>>7658297
They are not intuitively, they are empirical.

>>7658297
Omg dude you don't understand them? How stupid are you?

I independently discovered them on my own when I was only 6. Shits basic anon.

No but really don't feel dumb just cause you find something hard to understand that doesn't mean anything. Dumb people are people like the guy in that relativity thread who think an idea must be wrong just because they don't understand it.

Certainly you can understand them to some extent... it's just a matter of putting in the time. IQ means way less than being willing to sit down and concentrate, day after day.

How much you get out of it will vary. I have a master's degree and have worked with them for years, and I don't understand them fully, all the implications and so on. The world is really complicated.

op here

I somewhat understand the integral form

but the differential form confuses me a lot

>>7658297
Yes. You could probably get a reasonably smart child to understand them intuitively. The vector forms are much easier to understand and visualize.

>>7658297
Here, I'll throw it out there quick.

>The electric field points directly towards or away from electric charges, and only from electric charges.

>The magnetic field just curls around; it never converges or diverges at all. basically, there's no such thing as "magnetic charge."

>If the magnetic field at a point is changing, say from a moving magnet, the electric field curls clockwise around the direction it's changing in.

>If the electric field at a point is changing, say from a moving electric charge, the magnetic field curls counterclockwise around the direction it's changing in. If you've got a continuous stream of moving charges so you just get steady current, that makes a magnetic field too in the same way.

The differential form of Maxwell's equations expresses electricity and magnetism as a vector field. Think of currents in a stream - every point in the stream has a direction and magnitude of flow. A vector field gives every point in space a vector - an expression of direction and magnitude. (Think of a little arrow.)

E is the electric field; B is the magnetic field.

[math]\nabla \dot[/math] is the "divergence." It means you're taking a point in the field and seeing if, on average, the nearby arrows are pointing inwards or outwards. Imagine water flows again - negative divergence is like a drain, with more water flowing inwards than flowing outwards. Positive divergence is a source, with more water flowing outwards than inwards. And zero divergence means exactly as much water is entering as leaving, with no net inwards or outwards trend. Divergence is a number - it tells you how much it's pointing in or out.

[math]\nabla \times[/math] is the "curl." If divergence is net inwards or outwards current, curl is a net tendency for the currents to curl around a point. Imagine a whirlpool, or kids going around a carousel. Curl gives you a vector, pointing along the axis of rotation.

>>7658378
Whoops. [math] \nabla \cdot \vec{ V } [/math] is the divergence of a vector field V, and [math]\nabla \times \vec{ V} [/math] is its curl.

Also, if this seems confusing, it's a LOT easier to explain with pictures.

I grabbed some pics from http://www2.sjs.org/raulston/mvc.10/topic.6.lab.1.htm , and if you want a more detailed explanation of divergence and curl I'd check there instead.

This doesn't have any divergence or curl:
http://www2.sjs.org/raulston/mvc.10/Topic.6.Lab.1_files/image010.gif

This is what a field with negative divergence, but no curl, at a single point looks like: http://mathinsight.org/media/image/image/vector_field_implosion.png

This also has positive divergence:
http://www2.sjs.org/raulston/mvc.10/Topic.6.Lab.1_files/image014.gif

Divergence doesn't have to be constant, either. This is a field where the divergence at a point x, y is 2x + 2y:
http://www2.sjs.org/raulston/mvc.10/Topic.6.Lab.1_files/image020.gif

And this is what a field with positive curl, but no divergence, at a single point looks like:
http://www2.sjs.org/raulston/mvc.10/Topic.6.Lab.1_files/image023.gif

And this is a little tricky, but it also has curl; remember that curl doesn't just mean circulation. A little waterwheel placed at each point would still spin, because the currents on one side are stronger than the currents on the other.
http://www2.sjs.org/raulston/mvc.10/Topic.6.Lab.1_files/image028.gif

>>7658378
You made me comprehend basics of fluid mech. Thanks.

>>7658312
same here
integral form makes most sense to me

>>7658378
>no such thing as magnetic charge
....yet
we might find monopoles

File: BarMagField3(small).jpg (37KB, 300x474px) Image search: [Google]

37KB, 300x474px

>>7658312
>>7658814
If you are comfortable with the ideas of curl and divergence it's much simpler.
Take for example:
[math]\vec{\nabla}\cdot\vec{B}=0[/math]

This is essentially saying that the divergence of the magnetic vector field is always equal to zero. The divergence of a vector field is a measurement of the source and sink of the vector field. Since magnetic fields have no sources of sinks the divergence must equal zero

How does one "understand" an equation?

>>7658938
understand the relations, understand the reasoning behind it, stop being a spazoid