A 0.0075 V/m electric field creates a 3.9 mA current in a 1.0-mm-diameter wire. What material is the wire made of?

Verified step by step guidance

1. Determine the cross-sectional area of the wire. The diameter of the wire is given as 1.0 mm, so the radius is 0.5 mm or 0.0005 m. The cross-sectional area can be calculated using the formula: $A=\pi r^2$, where $r$ is the radius.
2. Calculate the current density, $J$, using the formula: $J=\frac{I}{A}$, where $I$ is the current (3.9 mA or 0.0039 A) and $A$ is the cross-sectional area calculated in the previous step.
3. Use Ohm's law in its microscopic form to relate the current density to the electric field: $J=\sigma E$, where $\sigma$ is the conductivity of the material and $E$ is the electric field (0.0075 V/m). Rearrange this equation to solve for the conductivity: $\sigma =\frac{J}{E}$.
4. Once the conductivity is calculated, compare it to known values of conductivity for various materials (e.g., copper, aluminum, etc.) to identify the material of the wire.
5. Verify the result by checking if the calculated conductivity matches the expected range for the identified material. This ensures the solution is consistent and accurate.

Key Concepts

Electric Field

An electric field is a region around a charged particle where a force would be exerted on other charged particles. It is quantified in volts per meter (V/m) and indicates the strength and direction of the force that a charge would experience. In this question, the electric field of 0.0075 V/m is responsible for driving the current through the wire.

Current

Electric current is the flow of electric charge, typically measured in amperes (A). In this scenario, a current of 3.9 mA (milliamperes) flows through the wire due to the applied electric field. The relationship between current, electric field, and material properties is crucial for determining the wire's conductivity.

Resistivity

Resistivity is a material property that quantifies how strongly a given material opposes the flow of electric current. It is typically measured in ohm-meters (Ω·m). The resistivity of the wire's material can be calculated using the current, electric field, and the wire's dimensions, allowing us to identify the material based on known resistivity values.