Magnetic constant mu0 doubled

Problem

Suppose the magnetic constant of the vacuum $\mu_0$ suddenly doubled. Discuss in five lines how the following would change: solenoid inductances, self-induced EMFs at fixed $\ddt{i}$, the speed of light.

Solution

Inductances. For a solenoid $L = \mu_0 N^2 A / \ell \propto \mu_0$: if $\mu_0$ doubles, every inductance doubles. Self-induced EMFs. $\mathcal{E} = -L\,\ddt{i} \propto L$: at fixed $\ddt{i}$, the self-induced EMF doubles as well. Speed of light. $c = 1/\sqrt{\mu_0 \varepsilon_0} \propto 1/\sqrt{\mu_0}$: doubling $\mu_0$, the speed of light drops by a factor $\sqrt{2}$. $L' = 2L, \qquad \mathcal{E}' = 2\mathcal{E}, \qquad c' = \frac{c}{\sqrt{2}}$

Links

Topics: Induzione elettromagnetica Concepts: Induttanza e autoinduzione Skills: Analisi di casi limite e fantafisica Objects: Solenoide