FirstPrinciplesa Physoly project
CIR-03circuitstrap · Dimensional inconsistency

Electric potential is not electric field

  1. 01

    The tempting model

    Using V and E interchangeably, or assuming E = 0 wherever V = 0.

  2. 02

    Why it feels right

    Both describe 'how strong the electricity is' in casual terms.

  3. 03

    Where it breaks · how to catch it

    You equated volts with volts per meter, or inferred one directly from the other's zero.

  4. 04

    The correct model

    Field is the negative gradient of potential: E_x = −dV/dx. V can be zero where E is nonzero, and V is constant throughout a region where E = 0.

  5. 05

    Repair · see it, then test it

    worked example At the midpoint between +q and −q, what are V and E?

    Tempting move

    Both zero.

    Correct move

    V = 0, but E is non-zero (points from + to −).

    Test the repair CIR-03 · transfer
    include V/m

    Make a fresh prediction before referring to the worked example.