The single most important use of the element gold is for...

The single most important use of the element gold is for wires that join integrated circuits to the conducting pads that then connect microelectronic chips with external circuitry. A typical application uses gold wires $1.0 \mathrm{mil}(0.001$ inch $)$ in diameter and $50 \mathrm{mil}$ long. Although the current under normal conditions is much less, such a wire will fuse (that is, melt and interrupt the current) when the current exceeds some $600 \mathrm{~mA}$. Find (a) the current density in the wire, (b) the electric field in the wire, and (c) the voltage between the ends of the wire, all when this maximum current is flowing.

Key Concepts

Current Density

Current density is defined as the amount of electric current flowing per unit cross-sectional area of a conductor. In problems involving conductors like the gold wires in microelectronics, the calculation of current density helps determine how intensely the current is distributed within the small wire diameter, which is crucial for understanding heating effects and potential fusing of the wire under high current conditions.

Electric Field in Conductors

The electric field in a conductor relates to how the electrical potential varies along the conductor and is connected to the current density through the material's conductivity. According to Ohm's microscopic law, the electric field can be calculated by dividing the current density by the conductivity of the material; alternatively, it reflects the local driving force that causes the charge carriers to move in the wire.

Ohm's Law and Voltage Drop

Ohm’s Law states that the voltage drop across a conductor is equal to the current flowing through it multiplied by its resistance. This relationship is fundamental to determining the voltage difference at the ends of the gold wire, as the resistance is influenced by factors such as the material's resistivity, the wire’s length, and its cross-sectional area. Calculating the voltage drop allows one to understand potential differences in microelectronic circuits during high current conditions.

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