Drift Velocity

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Drift velocity v_d relates to current I by I = ?

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1. **Theory**: Current is the total charge passing through a cross-section per unit time.
2. **Variables**:
   - $n$: Number density of free electrons (electrons/$m^3$).
   - $A$: Cross-sectional area of conductor ($m^2$).
   - $e$: Magnitude of electronic charge ($C$).
   - $v_d$: Average drift velocity ($m/s$).
3. **Derivation**: In time $\Delta t$, electrons travel a distance $v_d \Delta t$. The volume containing these electrons is $A v_d \Delta t$. Total charge $\Delta Q = (n \cdot A v_d \Delta t) \cdot e$. 
4. **Current Formula**: $I = \frac{\Delta Q}{\Delta t} = n A e v_d$.

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