GATE 2026 PH – Question 15
Which of the following options is correct for transformation of electric field $\mathbf E$ and magnetic field $\mathbf B$ under time reversal, i.e., $t\to-t$?
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Correct answer: (C) $\mathbf E\to\mathbf E$ and $\mathbf B\to-\mathbf B$
Explanation
Under **time reversal** $t\to-t$:
- positions and the charge density $\rho$ do not change;
- velocities and currents $\mathbf J$ reverse sign.
Maxwell's equations must keep their form. The Gauss law $\nabla\cdot\mathbf E=\rho/\epsilon_0$ has $\rho$ unchanged, so $\mathbf E$ is **unchanged**: $\mathbf E\to\mathbf E$.
In the Ampère law $\nabla\times\mathbf B=\mu_0\mathbf J+\mu_0\epsilon_0\partial_t\mathbf E$, the current $\mathbf J$ changes sign and the time derivative of $\mathbf E$ also changes sign, so $\mathbf B$ must change sign: $\mathbf B\to-\mathbf B$. (The Faraday law $\nabla\times\mathbf E=-\partial_t\mathbf B$ is consistent too: the left side is unchanged, and $\partial_t\mathbf B$ is unchanged when both $t$ and $\mathbf B$ change sign.)
Answer **$\mathbf E\to\mathbf E$ and $\mathbf B\to-\mathbf B$** (C).