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## Homework Statement

Given that (φ/c,

**A**) is a 4-vector, show that the electric field component Ex for a

Lorentz boost along the x-axis transforms according to Ex' = Ex.

## Homework Equations

[tex]E_x = -\frac{\partial \phi}{\partial x} - \frac{\partial A_x}{\partial t}[/tex]

[tex]A_x[/tex] being the x component of the vector potential

## The Attempt at a Solution

So I don't have a problem getting φ'/c or Ax'

Obviously:

[tex]E_x^{\prime} = -\frac{\partial \phi^{\prime}}{\partial x^{\prime}} - \frac{\partial A_x^{\prime}}{\partial t^{\prime}}[/tex]

But I don't understand how to get the partial derivative w.r.t. x' in terms of x and t. Likewise for the partial derivative w.r.t. t'.

In the solutions it seems:

[tex]\frac{\partial}{\partial x^{\prime}} = - \frac{\gamma \beta}{c}\frac{\partial}{\partial t} - \gamma \frac{\partial}{\partial x}[/tex]

?? Does it come from the lorentz co-ord transformation?