Key relationship
Ewire=λ/(2πε₀r); Esheet=σ/(2ε₀); Eshell=0 inside, kQ/r² outside.
Physics · Class 12
Gaussian wire, sheet and shell
Switch the charge geometry. A wire gives a 1/r field, an ideal sheet gives a distance-independent field, and a shell gives zero interior field.
Open the interactive experiment →Gaussian wire, sheet and shell
கம்பிப் புலம் 1/r ஆகக் குறையும். முடிவிலா தகட்டுப் புலம் மாறாது. கோள ஓட்டின் உள்ளே புலம் பூஜ்யம்.
Key notes, relationships and model limits
Remember
Switch the charge geometry. A wire gives a 1/r field, an ideal sheet gives a distance-independent field, and a shell gives zero interior field.
Common trap
The Gaussian result depends on symmetry. An infinite sheet, an infinite wire and a spherical shell are different geometries.
Model limits
Infinite wire/sheet and thin uniform spherical shell. Charge units change with selected geometry. Potential is modelled only for the shell, relative to infinity; infinite wire and sheet potentials require a separately chosen finite reference.
What you will learn
Use the controls and plotted relation to explain gaussian wire, sheet and shell.
Try the experiment
Try both scenarios, change one control, and predict the result before checking the graph and readouts.
Think of it this way
Change one input while keeping the others fixed, as you would in a controlled experiment.
Worked example
For Q=10 nC and shell radius 0.5 m, E=0 at r=0.25 m and ≈89.9 N/C at r=1 m.
Why this matters
The model connects gaussian wire, sheet and shell with an observable reading. Check the equation and assumptions before applying it.
Before you start
SI units · algebra · graph reading
Check your understanding
Inside a uniformly charged spherical shell, E equals?
- The same field as at the outer surface.
- Zero everywhere in the cavity.
- kQ/r² throughout the cavity.
Read the explanation
Zero everywhere in the cavity.
Course connection: Class XII Chapter 1. Consult the roadmap for CBSE, NEET, JEE Main and Advanced scope.