Correct Answer - Option 1 : σ = J/E
Concept:
Ohms’ law: At constant temperature, the current through a resistance is directly proportional to the potential difference across the resistance.
V = R I
Where V is the potential difference, R is resistance and I is current flowing
Current density (J): The electric current per unit area is called current density.
\(Current~density~\left( J \right)=\frac{Current~\left( I \right)}{Area~\left( A \right)}\)
Conductivity (σ): The property of a conductor due to which the current flows through it is called the conductivity of that conductor.
\(Resistance~\left( R \right)=\frac{\rho ~l}{A}\)
Where ρ is resistivity = 1/σ, l is the length and A is the area of the conductor
Electric field (E) = potential difference (V)/length (l)
Analysis:
As, V = R I
\(Resistance~\left( R \right)=\frac{\rho ~l}{A}\)
\(V=\frac{\rho ~l}{A}\times I=\left( \frac{1}{σ } \right)\times l\times \frac{I}{A}=\left( \frac{1}{σ } \right)\times l\times J\)
\(J=σ \times \frac{V}{l}=σ ~E\)
σ = J/E
