02 · Two sources, one field

Does the field cancel between equal opposite charges?

At a dipole midpoint, will potential and field both be zero?

Place equal +Q and −Q on opposite sides.
Inspect midpoint field and potential.
Change −Q to +Q and compare.

Measurement

Vector sum E=E₁+E₂ and scalar sum V=V₁+V₂.

Between opposite sources the field vectors align and add, while signed scalar potentials cancel at the midpoint. For equal like charges the midpoint field cancels instead. This is a practical linear-algebra distinction between scalar and vector addition.

Eᵢ is each field in N/C; V is potential in volts; rᵢ in m.

E = Σ Eᵢ; V = Σ kQᵢ/rᵢ; E = −∇V

Worked example 1

For ±1 nC at x=±1 m, midpoint |E|=17.98 N/C and V=0.

Worked example 2

For two +1 nC sources at the same locations, midpoint E=0 and V=17.98 V, before core softening.

Double one like charge and locate the new zero-field point.

Assumptions

Static sources and Coulomb superposition. A softened core regularises singularities. Field lines are visual constructions whose density depends on seeding. This is not a time-dependent Maxwell solver.

University Physics Volume 2, 5.4 Electric Field

University Physics Volume 2, 7.2 Electric Potential and Potential Difference