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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
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Solution
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.
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