A current-carrying gold wire has diameter 0.84 mm . The electric field in the wire is 0.49 V /

step 1 Right. So in this problem we have a golden wire. And we know that for this golden wire, the diam

A current-carrying gold wire has diameter 0.84 mm . The...

A current-carrying gold wire has diameter $0.84 \mathrm{~mm} .$ The electric field in the wire is $0.49 \mathrm{~V} / \mathrm{m}$. What are (a) the current carried by the wire; (b) the potential difference between two points in the wire $6.4 \mathrm{~m}$ apart; (c) the resistance of a $6.4 \mathrm{~m}$ length of this wire?

Key Concepts

Potential Difference Along a Conductor

The potential difference between two points in a conductor is obtained by multiplying the electric field by the distance between those points (?V = E × ?L). This concept allows one to determine the voltage drop over a specified segment of a wire.

Resistance of a Conductor

Resistance is a measure of the opposition a material offers to the flow of electric current. It is given by R = ?L/A, where ? is the material's resistivity, L is the length of the conductor, and A is its cross-sectional area. This relationship is fundamental to understanding how voltage drops occur along a conductor.

Electric Field in Conductors

The electric field inside a conductor represents the force per unit charge that drives the motion of charge carriers. It is related to the potential difference and the length of the conductor by the relation E = ?V/?L, and it plays a central role in inducing current.

Current Density and Ohm's Law

Current density is defined as the current per unit area (j = I/A) and has a direct relationship with the electric field through the material's conductivity, expressed as j = ?E. This microscopic form of Ohm's law links the applied electric field with the resulting current flow in the conductor.

Cross-Sectional Area Calculation

In problems involving wires, the cross-sectional area is key because many properties depend on it. The area is computed from the diameter or radius using the formula A = ?r². This calculation is used in determining the current density and the resistance of the wire.

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