The ratio of conduction current density to the displacement current density is a) σ / jωεb) jσ / ωεc) σω / jεd)σε / jω Select one:badc

To determine the ratio of conduction current density to displacement current density in the context of electromagnetism, we can start by recalling the relevant definitions.

1. Conduction Current Density (J): This is related to the electric field (E) and conductivity (σ) as follows: $J = \sigma E$

2. Displacement Current Density (D): The displacement current density can be defined in terms of the electric field and permittivity (ε) as: $D = \varepsilon \frac{\partial E}{\partial t} = j\omega \varepsilon E$ where $j$ is the imaginary unit and $\omega$ is the angular frequency.

Now let’s form the ratio of conduction current density (J) to displacement current density (D):

3. Ratio Calculation: $\frac{J}{D} = \frac{\sigma E}{j\omega \varepsilon E}$ Here, the $E$ term cancels out: $\frac{J}{D} = \frac{\sigma}{j\omega \varepsilon}$

Final Answer

The correct expression for the ratio of conduction current density to the displacement current density is: $\frac{J}{D} = \frac{\sigma}{j\omega \varepsilon}$ Thus, the answer is (a) $\frac{\sigma}{j\omega \varepsilon}$.