Question

Calculate the electric field in a copper wire of cross-sectional area 2.0 mm² carrying a current of 1 A.
The resistivity of copper = 1.7 × 10^–8 Ω m

Answer 1

Given:
Area of cross-section, A = 2 × 10^–6 m²
Current through the wire, i = 1 A
Resistivity of copper, ρ = 1.7 × 10^–8 Ωm
Resistance of a wire,
$R=\rho \frac{l}{A}$
Also from Ohm's Law, voltage across a wire,
$V=iR=\frac{i\rho l}{A}$
The electric field of the wire,
$$\begin{gathered} E=\frac{V}{l} \\ \Rightarrow E=\frac{i\rho l}{Al}=\frac{i\rho }{A} \\ \Rightarrow E=\frac{1\times 1.7\times {10}^{-8}}{2\times {10}^{-6}} \\ \Rightarrow E=8.5\mathrm{V}/\mathrm{m} \end{gathered}$$