Option 1: Band picture separating the three classes of solids
Step 1: When atoms crowd together in a crystal, their sharp energy levels smear into wide bands. The topmost occupied band is the valence band and the next allowed band is the conduction band; between them may lie a forbidden gap \(E_g\) where no electron states exist. Electrical conduction needs electrons that are free to accept energy in the conduction band.
Step 2: A metal is a natural conductor because either its conduction and valence bands overlap or its conduction band is only half full. There is effectively no gap to cross, so a sea of electrons drifts freely and resistance is low.
Step 3: An insulator has a filled valence band capped by an empty conduction band with a wide barrier, several electron-volts high. Thermal energy at room temperature is far too small to lift electrons across, so charge cannot flow.
Step 4: A semiconductor shares the insulator layout but its gap is narrow, near 1 eV. Modest heating (or doping) promotes a handful of electrons upward, each leaving a mobile hole, so it conducts weakly; warming it further frees more carriers, so its resistance falls with rising temperature.
Step 5: Ranking the gap widths captures everything: zero for conductors, about 1 eV for semiconductors, and above roughly 3 eV for insulators.
\[ \boxed{\;\text{conductor }(E_g\approx0)\;<\;\text{semiconductor }(\sim1\text{ eV})\;<\;\text{insulator }(\gtrsim3\text{ eV})\;} \]
Option 2: Three magnetic behaviours and the electromagnet analogy
Step 1: Diamagnetic substances lack any permanent atomic magnet. An applied field induces a tiny opposing moment (Lenz-like), so they are pushed gently out of strong-field regions; their susceptibility is small and negative and \(\mu_r\) is just below 1. Bismuth and copper are typical.
Step 2: Paramagnetic substances do carry permanent atomic moments but these point randomly. A field nudges them into partial alignment, producing a weak attraction; susceptibility is small and positive, \(\mu_r\) slightly above 1. Aluminium and platinum fit here.
Step 3: Ferromagnetic substances have neighbouring moments locked into domains. An external field swings whole domains around, giving intense magnetisation that survives after the field is removed; susceptibility is large and positive, \(\mu_r\) enormous. Iron, cobalt and nickel are the classic examples.
Step 4: Now consider a solenoid carrying current. Every loop is a magnetic dipole, and stacking many loops makes their axial fields reinforce, so a strong, nearly uniform field runs down the tube and loops back outside, matching a bar magnet's field exactly. The face where field lines stream out is the north pole and the opposite face is the south pole.
Step 5: Quantitatively the solenoid's dipole moment is \(m=NIA\) for \(N\) turns of area \(A\) carrying current \(I\); suspended freely it settles along the geographic north-south line, and reversing the current swaps its poles, confirming it truly acts as a bar magnet.
\[ \boxed{\;m=NIA\;} \]