Question

Explain the difference between conductor, insulator and semiconductor on the basis of energy band in solids.
OR
Define diamagnetic, paramagnetic and ferromagnetic materials. Explain that a current carrying solenoid behaves as a bar magnet.

Hint:

Compare the forbidden energy gap: zero for conductors, about 1 eV for semiconductors, more than 3 eV for insulators. For magnetism, classify by susceptibility sign/size and recall each solenoid turn is a dipole giving m = NIA.

Answer 1

Option 1: Conductors, insulators and semiconductors by energy bands

Step 1 (Energy bands): In a solid, the closely packed atoms make the discrete atomic energy levels spread into continuous bands. The highest band filled with valence electrons is the valence band; the next higher, normally empty, band is the conduction band. The gap between them is the forbidden energy gap \(E_g\). Only electrons in the conduction band (or with empty states available) can carry current.

Step 2 (Conductors): In conductors (metals) the valence band and conduction band overlap, or the conduction band is partly filled, so \(E_g\approx0\). A huge number of free electrons is available even at room temperature, giving very high conductivity.

Step 3 (Insulators): In insulators the valence band is completely full and the conduction band empty, separated by a large forbidden gap \((E_g>3\text{ eV},\) e.g. \(\approx6\text{ eV}\) for diamond\()\). At ordinary temperatures electrons cannot jump this gap, so no current flows.

Step 4 (Semiconductors): In semiconductors the band structure is like an insulator but the forbidden gap is small \((E_g\approx1\text{ eV};\) Si \(\approx1.1\text{ eV},\) Ge \(\approx0.7\text{ eV})\). At room temperature a few electrons gain enough thermal energy to cross into the conduction band, leaving holes behind, so the material conducts moderately. Conductivity rises with temperature (opposite to metals).

Step 5 (Summary): Conductor: no/overlapping gap, many free electrons. Insulator: large gap, no free electrons. Semiconductor: small gap, few carriers that increase with temperature or doping.
\[ \boxed{\;E_g:\ \text{conductor}\approx0\ <\ \text{semiconductor}\approx1\text{ eV}\ <\ \text{insulator}\gtrsim3\text{ eV}\;} \]

Option 2: Magnetic material types and solenoid as a bar magnet

Step 1 (Diamagnetic): Materials that are feebly repelled by a magnet. They have no net atomic magnetic moment; in an external field a weak moment is induced opposite to the field, so relative permeability \(\mu_r<1\) and susceptibility \(\chi\) is small and negative. Examples: bismuth, copper, water.

Step 2 (Paramagnetic): Materials that are feebly attracted by a magnet. Their atoms have a permanent magnetic moment; in an external field the moments align partly along the field, so \(\mu_r>1\) and \(\chi\) is small and positive. Examples: aluminium, platinum, oxygen.

Step 3 (Ferromagnetic): Materials that are strongly attracted and can be permanently magnetised. They contain domains that line up strongly with an external field, giving \(\mu_r\gg1\) and large positive \(\chi\). Examples: iron, cobalt, nickel.

Step 4 (Solenoid as a bar magnet): A solenoid is a long coil carrying current \(I\). Each turn acts as a magnetic dipole, and the fields of all the turns add along the axis. The magnetic field lines emerge from one end and enter the other, exactly like those of a bar magnet: the end from which lines emerge behaves as a north pole and the other as a south pole (found by the clock rule / right-hand rule).

Step 5 (Magnetic moment): For a solenoid of \(N\) turns, length carrying current \(I\) and cross-section area \(A\), the magnetic moment is \(m=NIA\), and the axial field far away is that of a bar magnet of the same moment. A freely suspended current solenoid also aligns north-south, confirming the analogy.
\[ \boxed{\;m=NIA\quad(\text{solenoid}\equiv\text{bar magnet})\;} \]