Electrical and Magnetic Properties of Solids Explained

Solids are not all alike inside: some carry electricity (copper wires), some block it (rubber insulation), and some are magnetic (fridge magnets) while others are not. The electrical and magnetic properties of solids come from how their electrons are arranged — whether electrons are free to move and whether their tiny magnetic moments line up or cancel out.

This matters because every electronic device depends on it: conductors for wiring, insulators for safety, semiconductors for chips, and magnetic materials for motors, hard drives and MRI machines. Choosing the right solid is the first step in all electrical engineering.

Key Concepts

• Conductors: resistivity ~10⁻⁸–10⁻⁶ Ω·m (copper: 1.7 × 10⁻⁸ Ω·m). Metals conduct because valence electrons are delocalised. Conductivity falls as temperature rises (vibrating ions scatter electrons).
• Insulators: resistivity above ~10¹⁰ Ω·m (rubber, glass, diamond). Their electrons are locked in filled bands with a huge energy gap.
• Semiconductors: resistivity between ~10⁻⁵ and 10⁶ Ω·m (silicon, germanium). Conductivity rises with temperature as more electrons jump the small band gap. Doping tunes it precisely.
• Diamagnetism: all paired electrons → weakly repelled by magnets (water, copper, bismuth). Present in every substance but very weak.
• Paramagnetism: unpaired electrons → weakly attracted to magnets (aluminium, oxygen). The effect disappears without the external field.
• Ferromagnetism: unpaired electrons in domains that align → strong permanent magnets (iron, cobalt, nickel below their Curie temperature, 1043 K for iron).

How It Works

1. Apply a voltage: in a metal, free electrons drift toward the positive terminal — current flows easily.
2. In an insulator, electrons cannot leave their atoms because the next available energy level is far away (large band gap) — no current flows.
3. In a semiconductor, a few electrons gain enough thermal energy to jump the small gap; heating or doping increases their number, so conductivity rises.
4. For magnetism: each electron is a tiny magnet. Paired electrons cancel (diamagnetic); unpaired ones add up.
5. In ferromagnets, quantum exchange forces align whole domains of atoms; an external field grows the aligned domains, leaving permanent magnetism.

Worked Example

A copper wire of length 2.0 m and cross-section 1.0 mm² carries current. Resistivity of copper ρ = 1.7 × 10⁻⁸ Ω·m. Find its resistance, and compare with a rubber cord of the same size (ρ ≈ 10¹³ Ω·m).

1. R = ρL/A. Area = 1.0 mm² = 1.0 × 10⁻⁶ m².
2. Copper: R = (1.7 × 10⁻⁸ × 2.0) / (1.0 × 10⁻⁶) = 0.034 Ω — nearly zero, an excellent conductor.
3. Rubber: R = (10¹³ × 2.0) / (1.0 × 10⁻⁶) = 2 × 10¹⁹ Ω — effectively infinite, a superb insulator.
4. The ratio is about 10²¹: this 21-orders-of-magnitude gap is why copper wires are coated in rubber.

Common Misconceptions

• "All metals are magnetic." Only iron, cobalt and nickel (and some alloys) are ferromagnetic at room temperature. Copper, aluminium and gold are not attracted to a fridge magnet — aluminium is weakly paramagnetic.
• "Heating a metal makes it conduct better." The opposite: heating increases ionic vibrations that scatter electrons, so metal conductivity falls with temperature. Semiconductors behave the other way.

Real-World Applications

• Power grids: aluminium and copper conductors carry electricity; ceramic and polymer insulators keep it safely on the towers.
• Electronics: doped silicon (semiconductor) is the basis of every transistor, diode and computer chip.
• Motors and data storage: ferromagnetic materials (neodymium magnets, ferrites) drive electric motors, speakers and hard-disk platters.

In short, conductivity spans 20+ orders of magnitude from copper to rubber, decided by electron mobility; magnetism spans from weak diamagnetism to strong ferromagnetism, decided by unpaired electrons and their alignment. Together they explain every electrical and magnetic material we use.