An aluminum wire with a diameter of 0.100 mm has a uniform...

An aluminum wire with a diameter of 0.100 mm has a uniform electric field of 0.200 V/m imposed along its entire length. The temperature of the wire is $50.0^{\circ} \mathrm{C}$ . Assume one free electron per atom. (a) Use the information in Table 27.2 to determine the resistivity of aluminum at this temperature. (b) What is the current density in the wire? (c) What is the total current in the wire? (d) What is the drift speed of the conduction electrons? (e) What potential difference must exist between the ends of a $2.00-\mathrm{m}$ length of the wire to produce the stated electric field?

Key Concepts

Resistivity

Resistivity is an intrinsic material property that quantifies how strongly the material opposes the flow of electric current. It is influenced by factors such as temperature and material composition, and understanding it is essential for predicting how metals conduct electricity under applied fields.

Conductivity

Conductivity is the reciprocal of resistivity and measures the ease with which electric charges move through a material. In metallic conductors, high conductivity arises from the large number of free conduction electrons, making it a central concept in analyzing current flow.

Electric Field

The electric field represents the force per unit charge acting on charged particles and is directly linked to the potential difference applied along a conductor. It sets the stage for electron motion, leading to the drift that underlies electrical conduction.

Current Density

Current density is defined as the amount of electrical current flowing per unit cross-sectional area of a conductor. It links the microscopic motion of charge carriers, such as electrons, to the macroscopic quantity of current, and is directly proportional to the electric field in a material with given conductivity.

Drift Velocity

Drift velocity is the average velocity attained by charge carriers (typically electrons) in a conductor when subjected to an electric field. Despite their high random thermal speeds, the net flow resulting from the field is slow and determines how quickly electrical energy is transported.

Ohm’s Law

Ohm's Law is a foundational principle that states the relationship between voltage, current, and resistance in electrical circuits. In its microscopic form, it connects the electric field and current density through the material's conductivity, providing a basis for understanding energy dissipation and conduction.

Free Electron Density

Free electron density refers to the number of electrons available to conduct electricity per unit volume in a material. In metals, this density is typically related to the number of atoms and the number of conduction electrons per atom, and it is crucial in calculating current transport and drift velocity.

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