Current is the Same at Every Cross-Section
One wire with three different thicknesses along it, and a counter at each. Squeeze the middle section and the carriers there speed up by exactly as much as the opening shrank, so all three counters keep climbing together. The current is never larger in the thin part.
Como usar esta simulação
- Drag the area slider to squeeze the middle section down to a quarter of its width
- Watch the three counters to check they stay level with one another
- Follow individual carriers as they speed up entering the narrow part and slow down leaving it
- Return the slider to full width to confirm all three drift speeds match again
O que observar
- All three counters rise at the same rate no matter how much the middle is squeezed
- Carriers visibly accelerate on entering the narrow section and slow again on leaving
- Halving the area doubles the drift velocity, leaving the product Av_d unchanged
- Charge never accumulates anywhere along the wire, which is why the rates must match
- Current density is larger in the thin part even though the current is identical
A física por trás
The current through a section is I = nAv_d e. In a single unbranched wire made of one material, n and e are fixed, so a narrower section can only carry the same current if the drift velocity rises in proportion — Av_d must stay constant. This is charge conservation stated locally: charge cannot pile up inside the wire, so whatever enters one end per second must leave the other end per second. A thin section has a higher drift velocity and a higher current density, but exactly the same current.