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Question

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


A
σ=E/j
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B
σ=j/E
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C
σ=jE
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D
σ=1/jE
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Solution

The correct option is B $$\sigma=j/E$$
Let I current flow through a conductor when applied potential difference V volt. then, from ohm’s law,
$$I=\dfrac VR$$
But $$R=\rho\dfrac LA$$
Therefore,
$$I=\dfrac V{\rho\dfrac LA} \\\implies \dfrac IA=\dfrac V{\rho L}$$
but, $$\dfrac IA=J, \dfrac VL=E$$
Hence, $$J=\sigma E\\\implies \sigma = \dfrac JE$$

Physics

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