The electric field E, current density J and conductivity $σ$ of a conductor are related as

Question

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Answer 1

Let I current flow through a conductor when applied potential difference V volt. then, from ohm’s law,
$I = \frac{V}{R}$
But $R = ρ \frac{L}{A}$
Therefore,
$I = \frac{V}{ρ \frac{L}{A}} ⟹ \frac{I}{A} = \frac{V}{ρ L}$
but, $\frac{I}{A} = J, \frac{V}{L} = E$
Hence, $J = σ E ⟹ σ = \frac{J}{E}$

Answer 2

Let I current flow through a conductor when applied potential difference V volt. then, from ohm’s law,

I = \frac{V}{R}

But

R = ρ \frac{L}{A}

Therefore,

I = \frac{V}{ρ \frac{L}{A}} ⟹ \frac{I}{A} = \frac{V}{ρ L}

but,

\frac{I}{A} = J, \frac{V}{L} = E

Hence,

J = σ E ⟹ σ = \frac{J}{E}