A shielding visible-over-screening boundary scan tests how the visible test charge compares with the screening cloud across rows, marking where the shielded field drops below the boundary the scan watches. The verdict is exact only for the stated charges, density, temperature, and shielding length in the ideal Debye model. Real plasmas add collisions, nonuniform fields, distribution functions, boundary/sheath effects, calibration, finite precision, and measurement uncertainty.

Visible charge walks through cancellation and sign reversal. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The checked row reaches finite cancellation

The diagram pins a six coulomb source and a negative six coulomb response. The visible ledger is zero before any boundary claim is made.

6 C+(−6 C)=0 C6\ \text{C}+(-6\ \text{C})=0\ \text{C}
Shielding boundary sourceSource, response, and visible charge are checked.sourcefieldresponse cloudsource=6 Cresponse=-6 Cvisible=0 Cscale2=12 m^2density=3lambda2=4 m^2

More negative response walks through the boundary

The source stays fixed. The response column moves from partial shielding to cancellation and then to a sign flip.

QsQrQvisible6−426−606−8−2\begin{array}{c|c|c}Q_s&Q_r&Q_{\text{visible}}\\6&-4&2\\6&-6&0\\6&-8&-2\\\end{array}
Visible charge boundary scanThe middle row is the checked source diagram.sourcefieldresponse cloudsource=6 Cresponse=-6 Cvisible=0 Cscale2=12 m^2density=3lambda2=4 m^2

Past zero, visible charge reverses sign

The last row is not a new particle model. It is the signed finite budget showing that over-response changes the sign of the outside ledger.

Qr<−QsQvisible<0\begin{array}{c}Q_r<-Q_s\\Q_{\text{visible}}<0\end{array}
Over-shielding sign boundaryThe checked zero row marks the sign boundary.sourcefieldresponse cloudsource=6 Cresponse=-6 Cvisible=0 Cscale2=12 m^2density=3lambda2=4 m^2