Systematic analogy between E and B

Many concepts of the magnetic field are obtained from those of the electric field through systematic substitutions. Keeping this column-by-column comparison in mind is the most effective conceptual guide for finding one’s way around magnetism: where electrostatics had $\varepsilon_0$ and charge $q$, magnetism has $\mu_0$ and charges in motion.

	Electric field $\vec{E}$	Magnetic field $\vec{B}$
Constant	$k = 9\cdot 10^9$, $\varepsilon_0 \approx 8{,}85\cdot 10^{-12}$	$\mu_0 = 4\pi\cdot 10^{-7}$
Point source	charge $q$ ($\pm$)	magnetic “charge” (N/S)
Monopoles	exist (electrons, protons…)	do not exist!
Field lines	open ($+\to-$)	always closed
Gauss (flux)	$\Phi_E = Q_\text{int}/\varepsilon_0$	$\Phi_B = 0$ (always)
Force on charge $q$	$\vec{F} = q\vec{E}$	$\vec{F} = q\,\vec{v}\times\vec{B}$

The analogies are deep but not complete, and it is precisely where they break down that the most interesting physics hides. Two differences stand out above all. The first: the electric force acts on any charge, at rest or in motion, whereas the magnetic force acts only on moving charges and in a direction perpendicular to the velocity. The second, even more radical, is the absence of magnetic monopoles: there is no isolated “magnetic charge” comparable to the electron. From this absence it follows that the lines of $\vec{B}$ are always closed and that the flux of $\vec{B}$ through any closed surface is zero.

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Topics: Magnetismo Concepts: Campo magnetico · Campo elettrico

Related exercises: Problema — Ampiezze dell’onda solare · Campo di un filo a 3 mm · Forza tra due fili paralleli concordi