Physic Labs

Electricity and magnetism

Electric field and field lines

Explore field lines and equipotentials of a point charge and a dipole; verify E=k∣Q∣/r2E = k|Q|/r^2 qualitatively through line density and the perpendicularity of the two families of curves.

High school

Equipment

  • Perspective canvas drawing field lines of the source charge
  • Button “Chuyển sang lưỡng cực” / “Chuyển sang điện tích điểm” (toggle dipole/point charge)
  • Sliders “Điện tích nguồn” (source charge) and “Khoảng cách lưỡng cực” (dipole separation)
  • Figure 2: family of equipotentials (blue) crossing field lines (orange), with readout

Procedure

  1. Observe field lines of a point charge

    In figure 1, drag «Điện tích nguồn» from 1 to 5 units and read the caption line: lines radiate uniformly and E grows in proportion to |q|. Drag the canvas to rotate; note the lines are denser near the charge — hinting the field is stronger near the source as in E=k∣Q∣/r2E = k|Q|/r^2.

  2. Switch to the dipole

    Click «Chuyển sang lưỡng cực» and read the new caption: field lines run from the positive to the negative charge. Drag «Khoảng cách lưỡng cực» from 0.30 m to 1.00 m; when the charges separate, the pattern approaches two independent radial fields, while close spacing favors curved lines bridging the poles. The total field is the superposition E⃗total=∑iE⃗i\vec E_{\text{total}} = \sum_i \vec E_i.

  3. Compare equipotentials and field lines

    In figure 2, read the caption: blue curves are equipotentials (constant V), orange curves follow E, and the two families cross at nearly right angles. Check this visually in both point-charge and dipole modes; explain it via E⃗=−∇⃗V\vec E = -\vec\nabla V — the field is always perpendicular to equipotential surfaces.

Simulation

Experiment history

From the 1830s, Michael Faraday introduced the idea of lines of force — first for electric and magnetic fields — to picture how action spreads through the space around a charged body rather than merely describing the force between two charges. In Experimental Researches in Electricity he drew lines radiating from positive charge and ending on negative charge, treating their curvature and density as signs of the field. Faraday’s “field” view was initially distrusted by many mathematically trained physicists for lacking formal notation; the young James Clerk Maxwell re-read Faraday’s accounts and translated them into equations in On Faraday’s Lines of Force (1856) and later work. In vector language, a point charge’s field follows the inverse-square law E=k∣Q∣/r2E = k|Q|/r^2 inherited from Coulomb, while equipotential surfaces cut field lines at right angles — exactly what this simulation displays.

Related physicists

Charles-Augustin de CoulombJames Clerk MaxwellMichael Faraday

Related library topics

Electric field and field lines