Question

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

A
σ=E/j
B
σ=j/E
C
σ=jE
D
σ=1/jE

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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