/sci/ - Science & Math

>electric field mode
>integral form: "The flux through a closed surface is directly proportional to the charge contained inside"
>differential form: "The divergence of E is proportional to local change density"
So charges generate electric field lines around them, right? Well the more field lines there are in a region, the stronger E is. If you imagine you have a chunk of charge and you draw a number of field lines radiating from it, then you draw an imaginary surface around it, you'll find that the number of field lines that exit the surface increases if you add more charge. Divergence is the spacial "explosiveness" of a vector field. The explosiveness is proportional to charge density. The integral and differential forms are equivalent because [math] \int_{\partial R}\mathbf{E}\cdot\hat{\mathbf{n}}\ \text{d}A=\int_R\nabla\cdot\mathbf{E}\ \text{d}V=Q_{enc}/\epsilon_0 [/math] by the divergence theorem, but [math] Q_{enc}=\int_R\rho\ \text{d}V [/math] which means they say the same thing.
>magnetic mode
>integral form: "Flux through a closed surface is always zero"
>differential form: "Divergence is zero"
It just so happens that whenever you draw a surface around a magnet, you get the same number of field lines entering as there are leaving the surface. It also turns out that you can write magnetic field as the curl of a vector potential: [math] \mathbf{B}=\nabla\times\mathbf{A} [/math]. Recall from basic vector calculus that the divergence of a curl is identically zero. Equivalence follows from divergence theorem. The "explosiveness" of a magnetic field is zero.
>>11584514
>2 point 000...0001 = 2
Yes.

>two sets of ears
Reminder that bottoms are a dime a dozen. Catboys can piss off too. saged and reported for off topic.