AcademyElectromagnetic Induction
Academy
Superconductivity
Level 1 - Physics topic page in Electromagnetic Induction.
Principle
Superconductors have zero dc resistance and expel magnetic flux below their critical conditions.
Notation
\(T_c\)
critical temperature
\(\mathrm{K}\)
\(B_c\)
critical magnetic field scale
\(\mathrm{T}\)
\(J_c\)
critical current density scale
\(\mathrm{A\,m^{-2}}\)
\(\Phi_0\)
magnetic flux quantum
\(\mathrm{Wb}\)
\(h\)
Planck constant
\(\mathrm{J\,s}\)
\(e\)
elementary charge
\(\mathrm{C}\)
Method
Derivation 1: Zero resistance is not the whole story
A perfect conductor would preserve whatever magnetic flux it had before resistance vanished. A superconductor actively expels magnetic field from its interior in the Meissner effect.
dc resistance
\[R=0\]
Interior field
\[B\approx0\quad\text{inside a bulk superconductor}\]
Derivation 2: Critical conditions
Superconductivity is destroyed when temperature, field, or current density exceeds material-dependent critical values.
Temperature condition
\[T<T_c\]
Field condition
\[B<B_c\]
Current condition
\[J<J_c\]
Derivation 3: Flux quantization
In superconducting rings, magnetic flux appears in discrete units because the coherent charge carriers have charge \(2e\).
Flux quantum
\[\Phi_0=\frac{h}{2e}\]
Allowed flux
\[\Phi=n\Phi_0\]
Rules
These are core superconductivity facts for induction contexts.
Zero resistance
\[R=0\]
Meissner interior
\[B\approx0\]
Flux quantum
\[\Phi_0=\frac{h}{2e}\]
Quantized flux
\[\Phi=n\Phi_0\]
Examples
Question
Why can a persistent current flow in a superconducting ring?
Answer
With
\[R=0\]
there is no ohmic power loss \(I^2R\), so a current can persist without a battery once established.Checks
- Zero resistance does not by itself explain the Meissner effect.
- Superconductivity only holds below critical temperature, field, and current limits.
- Flux quantization uses charge \(2e\), not \(e\).
- Type-II superconductors can admit quantized vortices between critical field values.