Current Density and Continuity
Current density is current per normal area for uniform flow. Charge conservation gives equal steady current through successive sections; for fixed carrier density, Av_d remains constant.
Why this shows up in the exam
Tapered conductors · Radially partitioned wire area · Comparing drift speeds in unequal sections
Learn the idea
Steady current is conserved through a series path even when area and drift speed change. A narrow part of a pipe makes a fixed flow move faster. Likewise, in a steady wire with no charge accumulating, the same current crosses every section while current density changes with area.
🧠 Memory hook: Same series current, smaller area, larger J and drift.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- J = I/A — uniform current density normal to area A
- I₁ = I₂ — steady-state continuity when no charge accumulates
- n₁ q A₁ v₁ = n₂ q A₂ v₂ — carrier-flow continuity across unlike sections
How to approach it
- 1Mark sections carrying the same current
- 2Calculate each actual area
- 3Use J or nqv only after continuity
Common slip-ups that cost marks
- •Setting current density equal in unequal areas
- •Using radius instead of area
- •Applying steady continuity during charge accumulation
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A cell of emf 6 V and internal resistance 1 ohm is connected to a 2 ohm resistor. Find the circuit current.
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