A copper wire has a square cross section 2.1 mm on a side. The wire is 4.3 m long and carries

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A copper wire has a square cross section 2.1 mm on a side....

A copper wire has a square cross section $2.1 \mathrm{~mm}$ on a side. The wire is $4.3 \mathrm{~m}$ long and carries a current of $3.6 \mathrm{~A} .$ The density of free electrons is $8.5 \times 10^{28} / \mathrm{m}^{3}$. Find the magnitudes of (a) the current density in the wire and (b) the electric field in the wire. (c) How much time is required for an electron to travel the length of the wire?

A copper wire has a square cross section $2.1 \mathrm{~mm}$ on a side. The wire is $4.3 \mathrm{~m}$ long and carries a current of $3.6 \mathrm{~A} .$ The density of free electrons is $8.5 \times 10^{28} / \mathrm{m}^{3}$. Find the magnitudes of (a) the current density in the wire and (b) the electric field in the wire.
(c) How much time is required for an electron to travel the length of the wire?

Key Concepts

Current Density

Current density is a measure of the electric current per unit cross-sectional area of a conductor. It is defined by the equation J = I/A, where I is the current flowing through the conductor and A is its cross-sectional area. This concept is essential in understanding how current is distributed over the area of a material, impacting how electric fields and forces act on the charge carriers within the conductor.

Ohm's Law in Differential Form (Electric Field in a Conductor)

Ohm's law in differential form relates the local electric field (E) within a material to the current density (J) through the material's conductivity (?) via the relation E = J/?. This formulation highlights that in a conductor, the electric field is directly responsible for driving the movement of charge carriers, and it helps in determining how much voltage is required to maintain a given current.

Drift Velocity

Drift velocity refers to the average velocity at which free charge carriers, such as electrons, move through a conductor when subjected to an electric field. It is related to the current density through the equation J = n e v_d, where n is the charge carrier density, e is the elementary charge, and v_d is the drift velocity. This concept is critical for understanding the microscopic behavior of electrons in response to applied electric fields.

Charge Carrier Density

Charge carrier density is the number of charge carriers per unit volume in a material. In conductors, it determines how many electrons are available to carry the electrical current. This parameter is a key factor in calculating both the current density and the drift velocity, linking the macroscopic current flow to the microscopic motion of electrons within the material.

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