How does charge sign affect field and force direction?
Will a negative test charge accelerate with or against the field?
- Place one positive source and inspect field arrows.
- Reverse its sign and release a test particle.
- Change the test charge and compare acceleration.
What to measure
E_x and E_y in N/C; F=qE in N.
The idea underneath
Field direction is defined using a positive test charge. A negative test charge feels the opposite force. The field itself depends on the sources, not the test charge.
E = kQ r/|r|³; F = qE; k ≈ 8.988×10⁹ N m²/C²Q is source charge, q test charge in C; r in m. 1 nC=10⁻⁹ C.
Build the argument
- Evaluate each source separately and add its vector contribution. Potential adds as a signed scalar.
- Use F = qE or F = q(v × B), then divide by mass to obtain acceleration.
- 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 Q=1 nC at r=1 m, E=8.99 N/C outward.
Worked example 2
In that field q=−2 nC gives F=−17.98 nN, toward the source. These unsoftened calculations apply away from the core.
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
What happens to field strength when distance triples?
Check your understanding
Where does a negative source’s field point?
- Toward the charge
- Away from the charge
Explanation
A positive test charge is attracted. Tripling distance reduces the unsoftened field to 1/9.
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.