A copper wire has radius 0.800 mm and carries current I at 20.0^∘ C. A silver wire with radius

step 1 Hi, in the given problem, radius of the copper wire is given as R -C -U is equal to 0 .80 millim

A copper wire has radius 0.800 mm and carries current I at...

A copper wire has radius $0.800 \mathrm{~mm}$ and carries current $I$ at $20.0^{\circ} \mathrm{C}$. A silver wire with radius $0.500 \mathrm{~mm}$ carries the same current and is also at $20.0^{\circ} \mathrm{C}$. Let $E_{\mathrm{Cu}}$ be the electric field in the copper wire and $E_{\mathrm{Ag}}$ be the electric field in the silver wire. What is the ratio $E_{\mathrm{Cu}} / E_{\mathrm{Ag}} ?$

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Key Concepts

Resistivity

Resistivity is an intrinsic property of a material that quantifies how strongly it opposes the flow of electric current. It is linked to the material’s structure and electron scattering mechanisms, and appears in the relation E = ?J, where a material with higher resistivity will develop a larger electric field for a given current density.

Current Density

Current density is defined as the electric current per unit cross?sectional area (J = I/A). It is crucial in determining the local electric field inside a conductor because, for a constant current, a smaller cross-sectional area results in a higher current density, leading to a higher electric field when multiplied by the resistivity.

Electric Field in Conductors

The electric field in a conductor is related to the current density and the material’s resistivity by the equation E = ?J. This relation implies that for conductors carrying the same current, the electric field will depend on both the intrinsic properties of the material (through resistivity) and the geometry of the conductor (through the cross-sectional area that determines current density).

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