Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 3 / 15D / b

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- Solution b

Solution

Transforming the electromagnetic field tensor by

F^{'} = Λ F Λ^{T}

and reading off its components gives

E_{1}^{'} = E_{1}, B_{1}^{'} = B_{1}, E_{2}^{'} = γ (E_{2} - v B_{3}), B_{2}^{'} = γ (B_{2} + \frac{v E _{3}}{c ^{2}}), E_{3}^{'} = γ (E_{3} + v B_{2}), B_{3}^{'} = γ (B_{3} - \frac{v E _{2}}{c ^{2}}) .

These are the parallel and transverse field transformation laws for a boost in the

x

direction.

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