17. Transforming the second, third and fourth Maxwell equations
Transforming the second Maxwell equation
We start transforming the second Maxwell equation. This is a vector equation:

Because of its complexity, we now finish the transformation componentbycomponent:
Note that 1/γ^{2} = 1 − β^{2} where β = V/c (see the definition of γ ).
Transformation of the third Maxwell equation
The third Maxwell equation transforms similarly to the first one above:
Transformation of the fourth Maxwell equation
The fourth Maxwell equation is a vector equation and will transform in a similar manner to the second Maxwell equation above. We start by transforming the left side of the fourth Maxwell equation:

Now we transform this componentbycomponent:
The right side of the fourth Maxwell equation is transformed as:

where we have used the relation: c^{2} = 1/(ε_{0}μ_{0} ) which can be solved for μ_{0}, i.e.: μ_{0} = 1/(c^{2}ε_{0}) .
Combining the above equations, we get:
