Correct Answer - Option 1 : Ohm's law
Concept:
Ohms’ law(General Definition)
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 the 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 an area of the conductor
Electric field (E) = potential difference (V)/length (l)
Explanation:
As V = R I
\(Resistance~\left( R \right)=\frac{\rho ~l}{A}\)
So,
\(V=\frac{\rho ~l}{A}\times I\)
\(\implies V =\left( \frac{1}{\sigma } \right)\times l\times \frac{I}{A}\)
\(\implies V=\left( \frac{1}{\sigma } \right)\times l\times J\)
\(\implies J=\sigma \times \frac{V}{l}=\sigma ~E\)
Now, Current density is actually a vector quantity and so is the electric field.
So, the given expression can be represented as
\(\overrightarrow{J} = \sigma \overrightarrow{E}\)
So, the correct option is Ohm's law.
