Displacement current in Maxwell equations

[snyski]

Does anyone know how to solve or at least how to begin solving the following problem?:

Prove that displacement current in the Maxwell equations can be neglected if characteristic time τ of changing electromagnetic field in the system satisfies to the following condition: τ >> L/c where L is the characteristic size of this system and c is light speed. (Hint: time derivative of some variable y can be approximated as ratio of its characteristic value to characteristic time, dy/dτ ≈ y/τ the similar approximation can be also used for spatial derivatives).

 

[scottie_000]

Can you write down the relevant Maxwell equation, then change all derivatives in length and time to simple division by their charactersitic values?

 

[snyski]

I believe I can use the following relation:

Defining the current density of J as the displacement current, by differentiating D with respect to time

(dD/dt)We get:

With B and E being defined as:

So instead of differentiating to time I can now simply divide by time? However, I don't quite see where light speed comes in and how I could prove the displacement current actually being neglectable.