A cylindrical wire of radius 0.5mm and conductivity 5 * 10⁷ S/m is subjected to an electric field of 10m V/m. The expected value of current in the wire will be x³πmA. The value of x is…………………..

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Vishal Baghel | Contributor-Level 10

6 months ago

radius r = 0.5 mm

$σ = 5 * 1 0^{7} s / m$

$\vec{E} = 10 * 1 0^{- 3} V / m = 1 0^{- 2} V / m$

As we know

$J = σ E$

$J = \frac{i}{A} = σ E$

$i = σ E A = 5 * 1 0^{7} * 1 0^{- 2} * π * {(0.5 * 1 0^{- 3})}^{2} = 1.25 π * 1 0^{- 1} A = 125 π m A = x^{3} π m A$

$∴$ x = 5

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