A 0.65-mm-diameter copper wire carries a tiny current of 3.2 μA. Estimate the current density.

검증된 단계별 안내

Determine the cross-sectional area of the copper wire. The wire is cylindrical, so the cross-sectional area can be calculated using the formula for the area of a circle:

A = π r 2^{2}

, where

r

is the radius of the wire. Convert the diameter (0.65 mm) to meters and divide by 2 to find the radius.

Substitute the radius into the formula for the area to calculate the cross-sectional area. Ensure that the units are consistent (meters for the radius).

Recall the formula for current density:

J = \frac{I}{A}

, where

J

is the current density,

I

is the current, and

A

is the cross-sectional area.

Substitute the given current (3.2 μA, converted to amperes) and the calculated cross-sectional area into the formula for current density.

Simplify the expression to find the current density. Ensure that the units are consistent, and express the result in standard units (A/m²).

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Current Density

Current density is defined as the amount of electric current flowing per unit area of a conductor. It is represented by the symbol 'J' and is calculated using the formula J = I/A, where 'I' is the current in amperes and 'A' is the cross-sectional area in square meters. Understanding current density is crucial for analyzing how current distributes within a conductor.

Cross-Sectional Area

The cross-sectional area of a wire is the area of a slice taken perpendicular to its length. For a cylindrical wire, this area can be calculated using the formula A = π(d/2)², where 'd' is the diameter of the wire. This concept is essential for determining how much current flows through a given area, which directly affects the current density.

Ohm's Law

Ohm's Law states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance of the conductor. It is expressed as V = IR, where 'V' is voltage, 'I' is current, and 'R' is resistance. This law helps in understanding the relationship between current, voltage, and resistance in electrical circuits.