03 · From voltage to motion
Is a field line a particle trajectory?
Will a particle with sideways velocity exactly follow a field line?
- Set up a dipole and show potential.
- Release a particle and compare its trajectory with the lines.
- Change initial velocity and compare paths in the same field.
Measurement
V in volts, U=qV in joules, particle position and speed.
A field line represents local direction. A particle carries momentum: acceleration follows qE/m, but velocity need not align with E. For a positive charge descending in potential, potential energy becomes kinetic energy. This distinction matters in electron optics.
U and K in J; q in C; V in volts; m in kg.
Worked example 1
A +2 nC charge falling through 10 V gains 20 nJ of kinetic energy.
Worked example 2
For m=10⁻⁹ kg, starting from rest gives v=√(2ΔK/m)=6.32 m/s.
Why can a negative charge gain kinetic energy while moving to higher voltage?
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, 7.2 Electric Potential and Potential Difference