CND-19

Meissner exponential

B(x) = B₀ e^{−x/λ}. Field expulsion at a superconducting surface.

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SuperconductivityMeissner

Governing equation

B(x)=B_0 e^{-x/\lambda}

$x \in \left[0, 800\right]$

where

B_0: External field (mT)
x: Depth (nm)
\lambda: Penetration (nm)
B: Field (mT)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

B(x)=B_0 e^{-x/\lambda}

$x \in \left[0, 800\right]$

$x = 0$ $B = 10$

Along the curve

②

Domain of the variable — blue

x_{\min} = 0,\quad x_{\max} = 800

$x \in \left[0, 800\right]$

$x = 0$ $x = 0$

Along the curve

③

Response curve — green

B(x)=B_0 e^{-x/\lambda}

$x \in \left[0, 800\right]$

$x = 0$ $B = 10$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}B}{\mathrm{d}x}

$x \in \left[0, 800\right]$

$x = 5.031$ $B^{\prime} = -0.117$

Along the curve

Lecture brief

Historical brief

Drude electrons, Bloch waves, BCS pairing (1957) and Wiedemann–Franz heat are the first solids-and-metals laws. The lab is conductivity, gap and phonon heat in closed form. This sheet (CND-19 — Meissner exponential) is the form associated with Meissner. Working symbols: $B_0$ , $x$ , $\lambda$ $\rightarrow$ $B$ . Perfect diamagnetism, not merely perfect conductivity. The hallmark of the Meissner state.

Purpose

Purpose: compute

B

from

B_0

x

\lambda

in Condensed matter via

B(x)=B_0 e^{-x/\lambda}

B(x) = B₀ e^{−x/λ}. Field expulsion at a superconducting surface. Use it when a real condensed matter question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

B_0 = 10.000\,\mathrm{mT}

x = 50.000\,\mathrm{nm}

\lambda = 80.000\,\mathrm{nm}

, the governing relation

B(x)=B_0 e^{-x/\lambda}

yields

B = 5.353\,\mathrm{mT}

. A surface, a dying B, a λ mark. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

External field B_010 mTDepth x50 nmPenetration \lambda80 nm

Outputs

Field B5.353 mT

Reading speed

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Narration of this film

A surface, a dying B, a λ mark.

Perfect diamagnetism, not merely perfect conductivity. The hallmark of the Meissner state.

Reading speed

Watch on YouTube