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Posted: **Wed May 04, 2022 1:49 pm**

: 4 Use The Lorentz Transformations 12 109 For The Electromagnetic Fields To Prove A That Both E B And E E C B B Are 1 (19.66 KiB) Viewed 70 times

: 4 Use The Lorentz Transformations 12 109 For The Electromagnetic Fields To Prove A That Both E B And E E C B B Are 2 (33.52 KiB) Viewed 70 times

4) Use the Lorentz transformations (12.109) for the electromagnetic fields to prove a) That both E-B and (E-E-c²B-B) are invariants. b) Suppose that at one point P in an inertial frame B = 0 but E#0. Is it possible to find another inertial frame in which the electric field is zero at P? c) Can you write these invariants in covariant forms in terms of the tensors F and G? That is, express them in forms that are manifestly invariants under Lorentz transformations. (See Problem 12.51.)
Here, then, Ēx = Ex, Ē, = y(Ey — vB₂), Bx = Bx, By = y (By + −1 E₂), Ē₂ = y(E₂ + vBy), B₂ = Y υ y ( B₂ - - - 2 Ey). (12.109)