Content

Metal and Current

Metal is shiny, smooth, malleable, carry current:conduct electricity. 𝑃=𝐼𝑉=𝐼²𝑅. Nonzero resistance. Wires radiate power away as heat. Electrons scatter off lattice, and lose energy. Reducing R is the target. Resistivity 𝜌=𝑅𝐴 and lower 𝑇→smaller 𝜌→smaller power loss.

Superconductor

Superconductor have R=0. Carry current perfectly. Do not lose energy. Current in a loop will run forever. Expel magnetic fields (Meissner effect).

Particles

Two kinds of particles:

• Fermions: spin 1/2, 3/2, 5/2 etc. Cannot occupy the same space at the same time. Pauli exclusion principle. Antisocial.
• Bosons: spin 0, 1, 2 etc. Can occupy the same space at the same time. All follow the crowd.

Pauli exclusion principle explains Why most matter cannot occupy the same space at the same time.
Bosons can occupy the same space at the same time. Photons are bosons, e.g. lasers. Helium is a boson →superfluidity.

Bose Condensation

At low temperature, bosons flock to the lowest level. Very stable state. Dissipationless flow. superfluidity, e.g. helium. Superconductivity, most metals do this at low 𝑇.

Superconductivity

Pair electrons→form bosons. Bosons condense into the lowest energy state. Lowest energy state cannot lose energy→electron pairs cannot dissipate energy. Dissipationless current flow. Lowest energy state cannot dissipate energy. That is excited atom release a photon to decrease the energy. While less excite atom release a photon to ground state. Atom in ground state cannot lose anymore energy→Quantum stability of ground state.

Mysteries of High Temperature Superconductors

Brittle, Creamic, Not shiny, Not metallic Magnetic inside, make your own. How they work is still a mystery.

Magnetic Flux through Superconducting ring.

Magnetic flux through superconducting ring cannot change. From Faraday's Law ∮ 𝐸⋅𝑑𝑙=−𝑑Φ_mag𝑑𝑡
Assume: ∮ 𝐸⋅𝑑𝑙≠0
Because 𝑅=0 in a superconductor, this would imply: 𝐼=|emf|𝑅→∞ and is impossible. Therefore 𝑑Φ_mag𝑑𝑡=0 must always be true for the flux through a superconducting ring.

Inductor

For a solenoid in steady state:𝐵=𝜇₀𝑁𝐼𝑑.
Let the current change→Induces emf in every loop:
emf_loop=𝑑Φ_mag𝑑𝑡=𝑑𝑑𝑡𝜇₀𝑁𝐼𝑑𝜋𝑅²=𝜇₀𝑁𝑑𝜋𝑅²𝑑𝐼𝑑𝑡 on each loop
emf_tot=𝑁(emf_loop)=𝜇₀𝑁²𝑑𝜋𝑅²𝑑𝐼𝑑𝑡 induced emf opposes the change

Inductance

Let inductance of solenoid 𝐿=𝜇₀𝑁²𝑑𝜋𝑅²⇒|emf_tot|=𝐿𝑑𝐼𝑑𝑡
Because of Faraday's Law, coils of wire take awhile to reach steady state.
|emf_tot|=𝐼*(resistance)=𝐿𝑑𝐼𝑑𝑡
𝐼=𝐼₀[1−𝑒^{−(resistance*𝑡/𝐿)}]=𝐼₀[1−𝑒^−𝑡/𝜏] where 𝜏=𝐿/(resistance)
The higher the inductance, the longer it takes to reach steady state and long time constant→inductors are used to filter out high-frequency noise.

Source and Reference

https://www.youtube.com/watch?v=gKWy9FVvkHY&list=PLZ6kagz8q0bvxaUKCe2RRvU_h7wtNNxxi&index=25