The electric field in a copper wire of cross-sectional area \( 4\,\mathrm{mm^{2}} \) carrying a current of 1 A and having electrical conductivity of \( 6.25\times10^{7}\,\mathrm{S\,m^{-1}} \), is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 4\times10^{-3}\,\mathrm{V\,m^{-1}} \)
Ohm's law in vector form is \( \vec{J} = \sigma\vec{E} \), where the current density is \( J = I/A \) and \( \sigma \) is the electrical conductivity.
\( \displaystyle E = \frac{J}{\sigma} = \frac{I}{A\,\sigma} \)
\( \displaystyle A = 4\,\mathrm{mm^{2}} = 4\times10^{-6}\,\mathrm{m^{2}} \)
\( \displaystyle E = \frac{1}{4\times10^{-6} \times 6.25\times10^{7}} = \frac{1}{250} = 4\times10^{-3}\,\mathrm{V\,m^{-1}} \)