Question

A copper wire of cross-sectional area $2.0m{m}^2$, resistivity $=1.7\times {10}^{-8}\Omega m$, carries a current of $1A$. The electric field in the copper wire is

• A. $8.5\times {10}^{-5}V/m$
• B. $8.5\times {10}^{-4}V/m$
• C. $8.5\times {10}^{-3}V/m$
• D. $8.5\times {10}^{-2}V/m$

Answer 1

The correct option is C $8.5\times {10}^{-3}V/m$

A copper wire of cross sectional area

$A=2.0{mm}^2$

$=2\times {\left({10}^{-3}\right)}^2$

$=2\times {10}^{-6}{m}^2$

resistivity $=\rho =1.7\times {10}^{-8}\Omega m$

carries a current at $I=1A$.

electric field in the copper wire

$R=D\frac{L}{A}⟶\left(1\right)$

where $R=$ resistance

$\rho =$ resistivity

$L=$ length

$A=$ area

$I=\frac{V}{R}$ (Using ohni's law) $⟶\left(2\right)$

$E=\frac{V}{q}⟶\left(3\right)$

where $E=$ electric field

$V=$ potential

$q=$ charge

$E=\frac{I\times R}{q}$

$=\frac{I\times P\times \frac{l}{A}}{q}$

$=\frac{1\times 1.7\times {10}^{-\delta }\times \frac{l}{2\times {10}^{-6}}}{9.6\times {10}^{-19}}$

$=\frac{1.7\times {10}^{-\delta }\times 10}{2\times {10}^{-6}\times 1.6\times {10}^{-19}\times 10}$

$=\frac{17}{32}\times {10}^{-8+6+119}$

$=8.5\times {10}^{-3}V/m$