Question

Which expression gives current density in terms of free electron density, relaxation time, and electric field?

Options

• \[j=\frac{neA}{v_d}\]

• \[j=\frac{ne^2\tau}{m}E\]

• \[j=\frac{eE\tau}{m}\]

• \[j=\frac{m}{ne^2\tau}E\]

Answer 1

Substituting the drift-velocity expression into the current-density relation gives \[j=\frac{ne^2\tau}{m}E\]. This is the microscopic form of Ohm’s law.