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,

\[E = \frac{V}{l}\]

Now:

`R = (fl)/A`

`= (1.7xx10^(-8)xxl)/(2xx10^-6)`

`V = iR = (1 xx1.7xx10^-8xxl)/(2xx10^-6)`

`E = (dV)/(dL) = V/l`

`= (1.7xx10^-8)/(2xx10^-6`

`= 1.7/2xx10^-2`

`= 17xx10^-3`

`= 8.5xx10^-3`mv/m.