Question

Write down the formula for the relation of current density, specific conductivity and the electric field.

Accepted Answer

Let $I$ current flow through a conductor when applied potential difference $V$ volt.

Then, from ohm’s law, $I = \frac{V}{R}$

That is, the voltage drop across two conductors is directly proportional to the flow of current

where $R$ is the proportionality constant and the resistance of the conductor which opposes the current flow. Now, the resistance of the conductor depends on the distance between the two plates of the conductor and the area of the plates. Let say, the distance between two plates is $L$ and area of the plates is $A,$ then

$R \propto \frac{L}{A} \Rightarrow R = \frac{ρ L}{A}$

Where $ρ$ is proportionality constant and known as resistivity. Now, the above value of $R$ can be substituted in the ohm’s law

$V = \frac{I ρ L}{A}$

Now here we can again substitute $j$ in place of $\frac{I}{A}$ as $j$ is the current density which gives us the current per area. $\Rightarrow V = jρ L$

Let the electric field across the conductor be $E$ , then the potential difference $V$ can be given as $V = E L$

We can substitute this value of $V$ in the above equation $\Rightarrow E L = jρ L$

$L$ from both sides get cancelled and we get

$\Rightarrow E = jρ j = \frac{E}{ρ}$

Hence, Current density $j = σE$

Where $σ$ is the conductivity and reciprocal of resistivity.

This is the required relation of current density, specific conductivity and the electric field.

Write down the formula for the relation of current density, specific conductivity and the electric field.

Important Questions on Current Electricity

Learn and Prepare for any exam you want !