Question

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

• A. $\sigma =E/j$
• B. $\sigma =j/E$
• C. $\sigma =jE$
• D. $\sigma =1/jE$

Answer 1

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,

$I=\frac{V}{R}$

But $R=\rho \frac{L}{A}$

Therefore,

$I=\frac{V}{\rho \frac{L}{A}}⟹\frac{I}{A}=\frac{V}{\rho L}$

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

Hence, $J=\sigma E⟹\sigma =\frac{J}{E}$