Problem — Science fiction physics — mu0 doubles

Problem

Suppose $\mu_0$ suddenly doubled, with $\varepsilon_0$ unchanged. How would $c$ change? And the travel time of light from the Sun to the Earth ($d=1{,}5\cdot 10^{11}$ m)? And the ratio $E_0/B_0$ in a plane wave?

Solution

New speed of light. From $c=1/\sqrt{\varepsilon_0\mu_0}$, substituting $\mu_0\to 2\mu_0$:

$c'=\frac{1}{\sqrt{\varepsilon_0\cdot 2\mu_0}}=\frac{c}{\sqrt2}\approx 2{,}12\cdot 10^8\ \text{m/s}$

Sun-Earth travel time.

$t=\frac{d}{c'}=\frac{1{,}5\cdot 10^{11}}{2{,}12\cdot 10^8}\approx 707\ \text{s}\approx 11{,}7\ \text{min}$

(compared with the current $\approx 8{,}3$ min: slower by a factor $\sqrt2$).

Ratio of the amplitudes. In a plane wave $E_0/B_0=c$, so:

$\ev{\frac{E_0}{B_0}=c'=\frac{c}{\sqrt2}}$

The ratio drops by a factor $\sqrt2$, exactly like the speed.

Collegamenti

Argomenti: Onde elettromagnetiche Concetti: Onda elettromagnetica Competenze: Analisi di casi limite e fantafisica