🛡️ Electromagnetic Shielding & Faraday Cage

A conductive shell redistributes charges to cancel the internal field. Skin depth δ = √(2/(ωμσ)) determines AC shielding. See field lines before and after the shield.

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Electric field lines (blue) and surface charges (±) · Toggle shield to compare

How it Works

When an external uniform electric field is applied to a grounded spherical conductor, free electrons redistribute on the surface until the superposition of the external field and the induced dipole field exactly cancels inside. The result: zero field inside the conductor and a distorted field pattern outside (field lines perpendicular to the surface, concentrated at the poles).

For AC fields, the field penetrates the conductor skin depth δ before being attenuated. The absorption shielding effectiveness A = 8.686 × t/δ dB increases with shield thickness t, conductivity σ, permeability μ, and frequency f. Choose different materials and frequencies to see how skin depth changes.

δ = √(2 / (ω × μ × σ)) [skin depth]
A = 8.686 × t / δ [absorption loss, dB]
E_inside = 0 [Faraday cage, static]
SE = A + R + correction [total shielding effectiveness]

Frequently Asked Questions

What is a Faraday cage?

A Faraday cage is a conductive enclosure that blocks external static or slowly-varying electric fields. When an external field is applied, free charges in the conductor redistribute on the surface until the internal field is exactly zero. Named after Michael Faraday who demonstrated it in 1836.

How does a Faraday cage block electric fields?

When an external electric field is applied to a conductive shell, free electrons redistribute on the outer surface to create an induced field exactly equal and opposite to the external field inside the conductor. The net internal field is zero by superposition. This happens nearly instantaneously for good conductors.

What is skin depth in electromagnetic shielding?

Skin depth δ = √(2/(ωμσ)) is the depth at which an AC electromagnetic field decays to 1/e (~37%) of its surface value. For copper at 1 MHz, δ ≈ 66 μm. A shield thicker than several skin depths provides excellent AC shielding.

Does a Faraday cage block magnetic fields?

A Faraday cage blocks electric fields perfectly but provides poor DC magnetic field shielding. For AC magnetic fields, changing flux induces eddy currents that oppose the field (Lenz's law). At high frequencies, eddy currents are strong enough to significantly attenuate the magnetic field.

What is shielding effectiveness (SE)?

SE = 20·log₁₀(E_incident/E_transmitted) in dB. It combines absorption loss A = 8.686·t/δ and reflection loss at the surface. A solid copper shield at 1 GHz has SE over 100 dB. EMC standards typically require 40–80 dB for equipment enclosures.

Why do Faraday cages have gaps and holes?

Real Faraday cages (like microwave oven doors with mesh) have gaps. As long as the gap size is much smaller than the wavelength of the signal being blocked, the shield remains effective. Seams, ventilation holes, and connector penetrations are the main weak points.

What materials are used for electromagnetic shielding?

Common shielding materials: copper (highest conductivity, σ = 5.8×10⁷ S/m), aluminum (lighter, σ = 3.5×10⁷ S/m), mu-metal (high permeability for magnetic shielding), conductive foam, and metallized fabrics for flexible applications.

How do you shield a magnetic field (MRI, transformers)?

For static or low-frequency magnetic fields, high-permeability materials like mu-metal redirect flux through the shield walls. Multiple layers with different permeabilities improve effectiveness. The shield must avoid magnetic saturation.

What is the difference between near-field and far-field shielding?

Near-field sources may be predominantly electric (high-impedance) or magnetic (low-impedance). Far-field plane waves have equal electric and magnetic components. Electric field shielding is easier; magnetic near-field shielding requires thick, high-permeability shields.

What is EMC and how does shielding help?

Electromagnetic Compatibility (EMC) ensures electronic devices neither emit harmful interference nor are susceptible to it. Shielding is one of the primary EMC techniques, along with filtering, grounding, and PCB layout. Standards like EN 55032, FCC Part 15 define emission limits that shielded enclosures help meet.

About this simulation

This simulation draws electric field lines bending around a conductive spherical shell, computing the exact dipole perturbation that a conducting sphere induces in a uniform external field. Toggling the shield on redistributes charges (shown as ± symbols) on the surface, collapses the field to exactly zero inside, and computes real skin-depth attenuation δ = √(2/(ωμσ)) for the material and frequency you choose.

🔬 What it shows

Electric field lines distorting around a shielded sphere with induced ± surface charges, an "E = 0 inside" zone, and live-computed skin depth δ, t/δ ratio, absorption shielding effectiveness SE = 8.686·t/δ dB, and residual internal field.

🎮 How to use

Set External Field E and Charge angle to orient the field, toggle Shield ON/OFF to compare, pick a Conductivity σ material (copper, aluminium, steel, conductive plastic), and adjust Frequency and Shield Thickness t to see skin depth and shielding effectiveness change live.

💡 Did you know?

Michael Faraday demonstrated this effect in 1836 by building a room lined with metal foil and showing that a powerful electrostatic generator outside produced no detectable field inside — the same principle now protects sensitive electronics inside a car during a lightning strike, since the car's metal body acts as a cage.

Frequently asked questions

Why do the field lines curve sharply around the shield instead of passing straight through?

The induced surface charges create a dipole field that exactly cancels the external field inside the sphere while distorting it outside, forcing field lines to bend and terminate perpendicular to the conductor's surface — this is the classic solution for a conducting sphere in a uniform field.

Why does switching to Conductive plastic dramatically increase skin depth?

Skin depth δ = √(2/(ωμσ)) is inversely proportional to the square root of conductivity σ, and conductive plastic has roughly 4 orders of magnitude lower σ than copper, so the field penetrates far deeper before attenuating — meaning a plastic shield of the same thickness gives much weaker shielding effectiveness.

Why does raising Frequency shrink the skin depth?

Skin depth also scales as 1/√ω, so higher-frequency fields are confined to an increasingly thin surface layer of the conductor. This is why even a thin copper shield can achieve very high shielding effectiveness at GHz frequencies while needing to be thicker at kHz frequencies.

What happens if I set Shield Thickness t much smaller than the skin depth?

The t/δ ratio drops below 1, and the absorption shielding effectiveness SE = 8.686·t/δ becomes small — meaning a thin shield lets a significant fraction of the external field leak through, which is why real enclosures need thickness of several skin depths for good attenuation.

Why does the Faraday cage only show "E = 0 inside" and not mention magnetic fields?

A static Faraday cage blocks electric fields essentially perfectly via surface charge redistribution, but it doesn't stop static (DC) magnetic fields the same way — magnetic shielding of that kind typically requires high-permeability materials like mu-metal rather than just a good conductor.