Two sources, one field

Does the field cancel between equal opposite charges?

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

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

What to measure

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

The idea underneath

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.

Build the argument

1. Evaluate each source separately and add its vector contribution. Potential adds as a signed scalar.
2. Use F = qE or F = q(v × B), then divide by mass to obtain acceleration.
3. The electric model uses consistent softened potential and field with ε = 0.2 m, so values very near a source differ from ideal point charges.

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.

Applications

Electrostatic lenses steer electrons; magnetic fields separate particles by momentum and charge. Both depend on vector direction as much as field strength.

Common misconception

A field line is not generally a particle path. A negative charge accelerates opposite E. A purely magnetic force does no work.

A further investigation

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

Check your understanding

Does V=0 imply E=0?

• Always
• No

Model limits

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