Question: Show by explicit calculation that the formulae for the charge and current densities of a collection of point charges, have exactly the same form when

Show by explicit calculation that the formulae for the charge and current densities of a collection of point charges,

N N p(r, t) = [qkd(r - rz(t)) and j(r, t) =

have exactly the same form when we boost from frame K to frame K' by a velocity v₀.

Show first thatby evaluating the Jacobian determinant in the volume element transformation

N N p(r, t) = [qkd(r - rz(t)) and j(r, t) = 9k Vk(t) 8(r - rk (t)), k=1 k=1

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To show that the charge and current densities have the same form when boosting from frame K to frame K by a velocity v0 we can use the Lorentz transformation to relate the quantities in the two frames ... View full answer

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