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Recently learnt about Maxwells Equations, am wondering what is the physical relation between electric field E and magnetic field B. It would help if the physical meanings are related to the mathematical symbols of the equations.

Additionally E is related to a fundamental force like the gravitational forces g but what really is B?

So g is related by F=mg as the gravitational force, and E is related by F=qE of the electric force, why would B be part of the Lorentz force?

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  • $\begingroup$ Could you elaborate on your last sentence? I'd say $\vec{E}$ and $\vec{B}$ are both related to a fundamental force - the Lorentz force $\vec{F}=q(\vec{E}+\vec{v}\times\vec{B})$. $\endgroup$ – jacob1729 May 24 at 9:00
  • $\begingroup$ @jacob1729 I have edited the last part of the question $\endgroup$ – 2569cfa May 24 at 9:14
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    $\begingroup$ I'm still confused why you think $\vec{E}$ is real, but imply that $\vec{B}$ is somehow not. $\vec{B}$ causes forces on charged particles that are moving via $\vec{F}=q\vec{v}\times\vec{B}$. $\endgroup$ – jacob1729 May 24 at 9:16
  • $\begingroup$ @jacob1729 I am confused about how does both of them together contribute to the electric force and why would that be true physically (not mathematically ) $\endgroup$ – 2569cfa May 24 at 9:20
  • $\begingroup$ I don't have time to write an answer right now. I think the key thing to look up are the Faraday tensor, which is a single object that contains all the information in both $\vec{E},\vec{B}$ as well as the behaviour of electromagnetic fields under Lorentz transforms. It turns out that 'mix' with each other in such a way that $\vec{E}+\vec{v}\times\vec{B}$ transforms in the same way as a force. $\endgroup$ – jacob1729 May 24 at 9:23
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If you were thinking about both $F_g$ and $F_e$ for a point mass or point charge went as $r^{-2}$. Sure, it's the well know connection.

However, notice that $F_{em}=q(E+\frac{1}{c} v\times B)$, so if you classify $F_g$ and $F_e$ as the "same" according to their simple mathematical structure without thinking, you'd classify $F_m$ as another set of equation.

Further, they were written in low energy limit. In orthodox physics, gravity was in GR and EM was was in the form of relativistic constrain, no where to be close to what you meant "fundamental". Also, notice that $E$ field could be written as scalar potential and written as the sum over Laurent series basis$\{r^i\}_{i=-\infty}^\infty$, again, no where to be near your form of "fundamental". If you written $E$ field in 3 vector or 4 vector complex form, you probably won't ask this question because then $EM$ directly arise from the wave solutions.

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