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GATE 2023 PH – Question 55

Nuclear and Particle Physics · conservation laws, isospin symmetry, charge conjugation, parity and time-reversal invariance. · 2 marks · Multiple select

Under parity and time reversal transformations, which of the following statements is(are) TRUE about the electric dipole moment p and the magnetic dipole moment μ ?

  1. p is odd under parity and μ is odd under time reversal
  2. p is odd under parity and μ is even under time reversal
  3. p is even under parity and μ is odd under time reversal
  4. p is even under parity and μ is even under time reversal

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Show answer and explanation

Correct answer: (A) p is odd under parity and μ is odd under time reversal

Explanation

Classify each dipole moment by its behaviour under parity (P: $\mathbf r\to-\mathbf r$) and time reversal (T: $t\to-t$).

**Electric dipole moment $\mathbf p=\sum q\mathbf r$:**
- Under parity, $\mathbf r\to-\mathbf r$ and charges are unchanged, so $\mathbf p$ is **odd** under parity (a polar vector).
- Under time reversal, positions and charges are unchanged, so $\mathbf p$ is **even** under T.

**Magnetic dipole moment $\boldsymbol\mu\propto\mathbf r\times\mathbf v$ (or $\mathbf L$, $\mathbf S$):**
- Under parity, $\mathbf r\to-\mathbf r$ and $\mathbf v\to-\mathbf v$, so the cross product is unchanged: $\boldsymbol\mu$ is **even** under parity (an axial vector).
- Under time reversal, $\mathbf v\to-\mathbf v$, so $\boldsymbol\mu$ is **odd** under T.

So the true statement is: **p is odd under parity and μ is odd under time reversal** (option A).