Sea water at frequency `v=4 xx 10^(8)` Hz has permittivity `epsilon ~~ 80 epsilon_(0)` permeability `mu= mu_(0)` and resistivity `rho= 0.25`M. Imagine a parallel plate capacitor immersed in sea water and driven by an alternating voltage source `V(t) =V_(0) " sin "(2pivt).` What fraction of the conduction current density is the displacement current density ?

Explanation

To solve the problem, we need to find the fraction of the conduction current density that is the displacement current density in a parallel plate capacitor immersed in seawater. We will follow these steps:

### Step 1: Define the given parameters
- Frequency, \( v = 4 \times 10^8 \) Hz
- Permittivity, \( \epsilon \approx 80 \epsilon_0 \)
- Permeability, \( \mu = \mu_0 \)
- Resistivity, \( \rho = 0.25 \, \text{M}\Omega \, \text{m} \)

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