Ordering materials by decreasing magnetic permeability (μr) Consider the following materials: 1) Nickel, 2) Silver, 3) Oxygen, 4) Aluminium. Arrange them in the order of decreasing relative permeability μr (highest first).

Introduction / Context:
Relative permeability μr indicates how a material responds to an applied magnetic field. Ferromagnets have μr ≫ 1, paramagnets have μr slightly greater than 1, and diamagnets have μr slightly less than 1. Ranking materials by μr helps in selecting cores, shields, and structural components in magnetic circuits.

Given Data / Assumptions:

• Nickel (ferromagnetic) exhibits very high μr depending on alloy and field.
• Aluminium is weakly paramagnetic (μr just above 1).
• Oxygen (notably O2 gas) is paramagnetic with μr slightly above 1.
• Silver is diamagnetic (μr slightly below 1).

Concept / Approach:

Order by categories first: ferromagnet > paramagnets > diamagnets. Among the two paramagnets listed, aluminium typically has a somewhat stronger positive susceptibility than oxygen under standard conditions, placing it ahead. Silver, being diamagnetic, is last. Therefore, the sequence is Nickel, Aluminium, Oxygen, Silver → 1, 4, 3, 2.

Step-by-Step Solution:

Verification / Alternative check:

Handbook susceptibilities show Ni ≫ 1; Al and O2 with small positive χ; Ag with small negative χ. This confirms the chosen order.

Why Other Options Are Wrong:

Options placing Silver ahead of Oxygen or Aluminium mis-rank a diamagnet above paramagnets; options that put Aluminium above Nickel ignore ferromagnetically large μr of Nickel.

Common Pitfalls:

Assuming all metals are ferromagnetic (most are not); forgetting that gases like O2 can be paramagnetic despite low density.

Final Answer:

1, 4, 3, 2