Discussion
Which of the following options is correct for transformation of electric field \(\vec{E}\) and magnetic field \(\vec{B}\) under time reversal, i.e., \(t \to -t\) ?
Answer: C
Under time reversal \(\vec{E} \to \vec{E}\) and \(\vec{B} \to -\vec{B}\).
Charges do not change under \(t \to -t\), and the electric field is fixed by where the charges are, so \(\vec{E}\) is unchanged. Currents are charges in motion; reversing time reverses every velocity, so every current reverses, and the magnetic field produced by currents changes sign.
The Lorentz force confirms this: \(\vec{F} = q(\vec{E} + \vec{v} \times \vec{B})\) is even under time reversal (it is mass times acceleration), and \(\vec{v}\) is odd, so \(\vec{B}\) must be odd while \(\vec{E}\) is even. The other three combinations break this invariance.
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