Question

The ratio of current density and electric field is called
A. Resistivity
B. Conductivity
C. Drift velocity
D. Mobility

Answer 1

Hint: With the use of the Ohm’s law we can establish the relationship between the current density j and the electric field E. The current density is the amount of current flowing through a particular charged area or flowing through the cross sectional area. Once we establish an expression for current density in terms of electric field, we can find the ratio.

Formula used:
\[\begin{align}
  & V=IR \\
 & j=\dfrac{I}{A} \\
 & j=\sigma E \\
\end{align}\]

Complete step-by-step answer:
We know that according to Ohm’s law
\[V=IR\]
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
\[\begin{align}
  & \Rightarrow R\propto \dfrac{l}{A} \\
 & \Rightarrow R=\dfrac{\rho l}{A} \\
\end{align}\]
Where ρ is proportionality constant and known as resistivity.
Now, the above value of R can be substituted in the ohm’s law
 \[V=\dfrac{I\rho l}{A}\]
Now here we can again substitute j in place of I/A as j is the current density which gives us the current per area.
\[\Rightarrow V=j\rho l\]
Let the electric field across the conductor be E, then the potential difference V can be given as
\[V=El\]
We can substitute this value of V in the above equation
\[\Rightarrow El=j\rho l\]
l from both sides get cancelled and we get’
\[\Rightarrow E=j\rho \]
Current density hence any also be given as
\[j=\sigma E\]
Where σ is the conductivity and reciprocal of resistivity.
Hence, the ratio of current density and the electric field is conductivity.

So, the correct answer is “Option B”.

Note: Here, the ratio of current density to electric field is asked therefore it is conductivity but if it was asked the vice versa that is the ratio of electric field to current density then the answer would be resistivity. Conductivity tells us the capacity to conduct whereas resistivity tells us the capacity to resist the follow of charges. Hence conductivity is a reciprocal of resistivity.