HI guys first post(adsbygoogle = window.adsbygoogle || []).push({});

I need to show that

[tex]B^2-E^2/C^2[/tex] is invariant under Lorentz transformation (E and B are electromagnetic fields)

now:

[tex]B^2-E^2/C^2=B^2_x+B^2_y+B^2_z-E^2_x/C^2-E^2_y/C^2-E^2_z/C^2)[/tex]

and

[tex]E'_x=E_x[/tex]

[tex]E'_y=\gamma(E_y-\frac{v}{c}B_z)[/tex]

[tex]E'_z=\gamma(E_z-\frac{v}{c}B_y)[/tex]

[tex]B'_x=B_x[/tex]

[tex]B'_y=\gamma(B_y+\frac{v}{c}E_z)[/tex]

[tex]B'_z=\gamma(B_z+\frac{v}{c}E_y)[/tex]

but i cant manupilate it to give me the correct answer ie

[tex]B'^2-E'^2/C^2=B^2_x+B^2_y+B^2_z-E^2_x/C^2-E^2_y/C^2-E^2_z/C^2[/tex]

Can anyone help me out? Basically because of the [tex]\gamma^2[/tex] term im tring to factorise out a [tex]1-\frac{v^2}{C^2}[/tex] ie [tex](1/\gamma^2)[/tex] but im having no joy.

**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!

# Invariant under Lorentz transformation

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