An 18 -gauge copper wire (diameter 1.02 mm ) carries a current with a current density of 1.50 ×1

step 1 Okay, so we know the current density, which is j here, can be equal to current divided by area.

An 18 -gauge copper wire (diameter 1.02 mm ) carries a...

An 18 -gauge copper wire (diameter 1.02 $\mathrm{mm} )$ carries a current with a current density of $1.50 \times 10^{6} \mathrm{A} / \mathrm{m}^{2} .$ The density of free electrons for copper is $8.5 \times 10^{28}$ electrons per cubic meter. ,Calculate (a) the current in the wire and (b) the drift velocity of electrons in the wire.

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Key Concepts

Current Density

Current density is defined as the amount of electrical current flowing per unit area of a conductor. It relates to the overall current by the equation I = J × A, where I is the current, J is the current density, and A is the cross-sectional area of the wire.

Cross-sectional Area Calculation

The cross-sectional area of a conductor, particularly a wire with a circular cross-section, is fundamental in computing electrical properties and is determined using the formula for the area of a circle (A = ?r²). This area directly influences the current when the current density is known.

Drift Velocity

Drift velocity is the average velocity with which charge carriers, such as electrons in a conductor, move under the influence of an electric field. It is related to the current through the relation I = n q v_d A, where n is the free charge carrier density, q is the elementary charge, v_d is the drift velocity, and A is the conductor's cross-sectional area.

Free Electron Density

Free electron density refers to the number of conduction electrons per unit volume in a material like copper. This parameter is essential in determining how effectively a material can carry current, as it quantifies the available charge carriers that contribute to electrical conduction.

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