Exercise 25.4 An 18-gauge copper wire (diameter 1.02 mm ) carries a current with

Question

Exercise 25.4

An 18-gauge copper wire (diameter 1.02 mm ) carries a current with a current density of 2.70 × 106 A/m2. The density of free electrons for copper is 8.5 × 1028 electrons per cubic meter.

Part A

Calculate the current in the wire.

Express your answer with the appropriate units.

Part B

Calculate the magnitude of the drift velocity of electrons in the wire.

Express your answer with the appropriate units.

Exercise 25.4

An 18-gauge copper wire (diameter 1.02 mm ) carries a current with a current density of 2.70 × 106 A/m2. The density of free electrons for copper is 8.5 × 1028 electrons per cubic meter.

Part A

Calculate the current in the wire.

Express your answer with the appropriate units.

Part B

Calculate the magnitude of the drift velocity of electrons in the wire.

Express your answer with the appropriate units.

Explanation / Answer

Part A:

since J = I / A then I = J * A

J is given and A is calculated as pi*diameter squared all over 4.

I = (2.7x10^6)(pi)(D^2)/4

I = 2.206 Amperes


Part B:

Since J = I / A = n*q*Vd

then Vd = J / n*q

Vd = 2.7x10^6 / ( 8.85x10^28)(1.6x10^-19)

Vd = 1.90x10^-4 m/s

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