In Einstein's paper section 6 (I'm reading an English version online: https://www.fourmilab.ch/etexts/einstein/specrel/www/), it's said that one of the Maxwell Equations in frame [itex]K[/itex](adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{1}{c}\frac{\partial X}{\partial t} = \frac{\partial N}{\partial y} - \frac{\partial M}{\partial z}[/tex], where [itex]<X, Y, Z>[/itex] denotes the vector of the electric force and [itex]<L, M, N>[/itex] that of the magnetic force, can be "transformed" into frame [itex]K'[/itex] which is moving at a constant speed [itex]v[/itex] on the [itex]x-axis[/itex] with respect to [itex]K[/itex],

[tex]\frac{1}{c}\frac{\partial X}{\partial \tau} = \frac{\partial}{\partial \eta} \{ \beta \cdot (N - \frac{v}{c}Y) \} - \frac{\partial}{\partial \zeta} \{ \beta \cdot (M + \frac{v}{c}Z) \} [/tex], where [itex]\beta = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}[/itex]

I'm confused by the existence of terms [itex]\frac{\partial Y}{\partial \eta}[/itex] and [itex]\frac{\partial Z}{\partial \zeta}[/itex], because it's derived in section 3 that

[tex]\tau = \beta \cdot (t - \frac{vx}{c^2})[/tex]

[tex]\xi = \beta \cdot (x - vt)[/tex]

[tex]\eta = y[/tex]

[tex]\zeta = z[/tex]

I can't find a way to apply partial derivative operations to make [itex]\frac{\partial Y}{\partial \eta}[/itex] and [itex]\frac{\partial Z}{\partial \zeta}[/itex] come out. Could anyone give me some tips? Any help is appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# [Special Relativity]Questions on Maxwell Equations' Derivation

Tags:

**Physics Forums | Science Articles, Homework Help, Discussion**