What is the microscopic expression for current density (J) in terms of electron charge (e), free electron number density (n), and drift velocity (vd)?
Answer and explanation
Correct answer: D. J = n e vd
- Step 1: Electric current is the total charge passing through a cross-sectional area per unit time: .
- Step 2: Current density is defined as current per unit cross-sectional area perpendicular to flow: .
- Step 3: Substituting : .
- Step 4: In vector form, (since electrons carry negative charge , drift velocity is opposite to current density).
Answer
J = n e vd
Why not the others: 'J = n e / vd' has dimensionally incorrect units; 'J = n e^2 vd' includes an extra charge factor; 'J = e vd / n' inverts carrier density.
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