How do I show the identity
?
>>10557318I think the key is what you are integrating over
Flux is stuff moving through an area (dS)
>One way to better understand the concept of flux in electromagnetism is by comparing it to a butterfly net. The amount of air moving through the net at any given instant in time is the flux. If the wind speed is high, then the flux through the net is large. If the net is made bigger, then the flux is larger even though the wind speed is the same. For the most air to move through the net, the opening of the net must be facing the direction the wind is blowing. If the net is parallel to the wind, then no wind will be moving through the net. The simplest way to think of flux is "how much air goes through the net", where the air is a velocity field and the net is the boundary of an imaginary surface.I don't get what you mean with the law of conservation sentences
>>10557343Well look at it this way
We know that energy is conserved always
Now consider you take a big rock in your arms and walk up a stair and place down the rock and walk down again
You obviously expended energy, we could write down integrals for that, dW = F.ds
What matters is that your energy is lowered
But yet, the total energy is conserved! How does that work?!
It works because we look only at the system that is you, in which energy is not conserved
But in the system that is the universe, energy is conserved
We don't even have to go that big, we can just look at the you-rock system
You lost energy but the rock gained energy, your energy
Assuming perfect everything the rock gained all of the energy that you expended
So energy is not conserved in the you system, nor in the rock system, but it is in the you-rock system
I don't know what you mean with your flux = 0 but I hope this makes it a bit clearer
