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.

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# Invariant under Lorentz transformation

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