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A steady current flows through an ohmic conductor of non-uniform cross-section. Which of the following quantities remain the same (independent of cross-section) at all points along the conductor?

1. The electric charge crossing any cross-section in a given time interval
2. Drift speed of electrons
3. Current density
4. Free-electron number density

Correct answer: The electric charge crossing any cross-section in a given time interval

Solution

By conservation of charge (steady state), the current I is the same at every cross-section. So the charge Q = I*t crossing any section in time t is constant — (A) is independent of cross-section. Drift speed v_d = I/(nAe) varies with A, so (B) is NOT independent. Current density J = I/A also varies with A, so (C) is NOT independent. Free-electron density n is a material property (number of conduction electrons per unit volume) and does not change with cross-section shape — (D) is independent. Correct answers: A and D.

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