Physic Labs

Electrodynamics

Electrostatic fields, conductors, and dielectrics

Compare electrostatic field structure and dielectric polarization across two illustrative figures; check qualitatively E∝1/r2E \propto 1/r^2, Einside conductor=0E_{\text{inside conductor}} = 0, and D=ε0εrED = \varepsilon_0\varepsilon_r E.

Undergraduate

Equipment

  • 3D canvas of the electrostatic field with buttons “Mô hình A”, “Mô hình B”, and “Tạm dừng”
  • Sliders “Biên độ / nguồn” (amplitude/source) and “Bước sóng / tỉ lệ” (scale)
  • Figure 2: polarized-dielectric field with sliders “Tần số / vận tốc” and “Góc nhìn / hệ số”
  • Readout lines plus the formula note “E ~ 1/r²; E inside = 0; D = ε₀εᵣE”

Procedure

  1. Inspect the electrostatic field structure

    In figure 1, compare the two setups with the buttons «Mô hình A» / «Mô hình B», drag to rotate the view, then press «Tạm dừng» to freeze the motion and inspect the field pattern. Read the line “E ~ 1/r²; vật dẫn cân bằng có E trong = 0; …” and note how the region near the source is denser than far away.

  2. Vary parameters and read the scaling

    Drag «Biên độ / nguồn» and «Bước sóng / tỉ lệ», watching the readouts a and k together with the changing field. Note that the field falls off with distance consistent with E∝1/r2E \propto 1/r^2, and that inside an equilibrium conductor the total field vanishes because surface charges rearrange to cancel the applied field.

  3. Analyze the polarized dielectric

    In figure 2, adjust «Tần số / vận tốc» and «Góc nhìn / hệ số»; read “D = ε₀εᵣE; góc điều khiển θ = …” and compare the field pattern inside the dielectric with outside. Interpret through D=ε0εrED = \varepsilon_0\varepsilon_r E: the dielectric weakens the field within it by εr\varepsilon_r, like a conductor expelling field — but only partially, since the material merely polarizes.

  4. Compare both models and predict

    Toggle «Mô hình A»/«Mô hình B» in figure 1 and record differences in the field-line pattern; then press «Chạy tiếp» to resume motion. Before setting «Góc nhìn / hệ số» in figure 2 to 0° and 90°, predict how θ and the field shape will change, then verify against the readout.

Simulation

Experiment history

In 1836 Michael Faraday built the metal cage now named for him to show that charge resides on a conductor’s outer surface while its hollow interior is screened from electric fields. He also studied “dielectrics” — insulating materials that polarize in a field — and used lines of force to picture how a medium transmits electric interaction. Henry Cavendish had earlier (about 1773) shown that his hollow-conducting-sphere experiment implies the inverse-square force law, though the result went unpublished; Maxwell recovered and extended it while directing the Cavendish Laboratory from 1870. In A Treatise on Electricity and Magnetism (1873), Maxwell introduced the electric displacement D=ε0εrED = \varepsilon_0\varepsilon_r E, separating the field set by free charge from the material’s polarization response — the framework still used for conductors and dielectrics.

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