Question: (a) Use the transformation laws for E and B to show that E B is a Lorentz invariant. (b) Find the boost velocity v
(a) Use the transformation laws for E and B to show that E · B is a Lorentz invariant.
(b) Find the boost velocity v from K to K' so that the field is purely electric or purely magnetic in K if E⊥B and E = cB in S.
(c) Static fields E = E0 ˆy and cB = E0(ŷ cos θ + ẑ sin θ) exist in some inertial frame S. Find the boost velocities from K to K' which make E' either parallel or anti-parallel to B' in K'. For both cases, find the θ dependence of the magnitudes of E',B', and the boost velocity.
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a To show that the dot product E B is a Lorentz invariant we need to demonstrate that it has the same value in all inertial reference frames Lets consider two inertial frames S and S where S is moving ... View full answer
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