Feeling a dipole's electric field along an ellipse: 2.08kq at the end, 0.13kq on top
TinfoilTricorn · x · 2026-10-14
Matharium walks through superposition E = kq r̂/r²: with +q at (−3,0) and −q at (3,0), a test charge on the ellipse x²/2.3² + y²/2² = 1 feels kq r̂₁/d₁² − kq r̂₂/d₂², where d₁² − d₂² = 12x.
At (2.3, 0) both pulls align to give 2.08kq; at the top of the ellipse the vertical components cancel, leaving 6kq/(13√13) ≈ 0.13kq parallel to the axis.
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