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The figure schematically shows the \(M\) (magnetization) - \(H\) (magnetic field) plots for certain types of materials. Here \(M\) and \(H\) are plotted in the same scale and units. Which one of the following is the most appropriate combination?

M against H on a square grid: line P has a small positive slope, Q a small negative slope, R a slope of minus one, and S a very steep negative slope

  • A.(Q) - Paramagnet; (R) - Type-I Superconductor; (S) - Antiferromagnet
  • B.(P) - Paramagnet; (Q) - Diamagnet; (R) - Type-I Superconductor
  • C.(P) - Paramagnet; (Q) - Antiferromagnet; (R) - Type-I Superconductor
  • D.(P) - Diamagnet; (R) - Paramagnet; (S) - Type-I Superconductor

Answer: B

The combination is (P) - Paramagnet; (Q) - Diamagnet; (R) - Type-I Superconductor.

The slope of each line is the susceptibility \(\chi = M/H\). P has a small positive slope, the weak positive response of a paramagnet. Q has a small negative slope, the weak opposing response of a diamagnet. R has a slope of exactly -1, so \(M = -H\) and \(B = \mu_{0}(H + M) = 0\): perfect diamagnetism, the Meissner state of a Type-I superconductor.

S is steeper than -1, a susceptibility below -1, which no material shows in equilibrium. An antiferromagnet has a small positive susceptibility, so calling Q an antiferromagnet is wrong, and the options assigning S to an antiferromagnet or a Type-I superconductor, or calling P diamagnetic, fail as well.

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