SHOW YOUR COMPLETE SOLUTION. MUCH BETTER IF YOU'LL WRITE THE SOLUTION ON A PAPER.2. Invariance of the wave equation. From the Maxwell's equations in vacuum, the fields, F = E, B satisfy the wave equation at2 F(x, t) = 0. (1) (a) [5 pts.] Show that under the Galilean transformation (t, I) - (t', I') ( ) - (48 9) (* ) (2) at a fixed field point in spacetime, F(x, t) = F(x', t'), the wave equation transforms into (1 - 32 ) 22 22 22 27-/2 + 2B ax'at' 21/2 F(x', t') = 0. (3) Thus, it is not invariant under Galilean transformation. (Hint: recall chain rule for partial derivatives.) (b) [5 pts.] On the other hand, show that the wave equation is invariant under the Lorentz transformation (t, x) -> (t', x') ( * ) = (-87 - B7) ( ). (4) 1 - 32