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A silver wire has resistivity 1.62*10⁻⁸ ohm*m and cross-sectional area 5.00 mm². The current in the wire is uniform and is increasing at the rate 2000 A/s at the instant the current equals 100 A. Which of the following statements is correct?

1. the magnitude of the uniform electric field in the wire when the current is 100 A is 0.324 V/m
2. the displacement current in the wire at that instant is 2.87*10⁻¹⁶ A
3. the ratio of the magnetic field from the displacement current to that from the conduction current at distance r is 2.87*10⁻¹⁸
4. the displacement-current density lines are straight, not circular

Correct answer: the magnitude of the uniform electric field in the wire when the current is 100 A is 0.324 V/m

Solution

Inside a current-carrying conductor, E = rho*J = rho*I/A. With rho = 1.62e-8 ohm*m, I = 100 A, A = 5.00e-6 m²: J = 100/5e-6 = 2e7 A/m², so E = 1.62e-8 * 2e7 = 0.324 V/m. This is the correct statement.

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