Topic: Electromagnetics
A material has conductivity of $10^{-2}\text{ mho/m}$ and a relative permittivity of 4. The frequency at which the conduction current in the medium is equal to the displacement current is
- A. 45 MHz
- B. 90 MHz
- C. 450 MHz
- D. 900 MHz
Answer: A. 45 MHz
Explanation: Conduction current density equals displacement current density when $\sigma = \omega \epsilon$.
$f = \frac{\sigma}{2\pi \epsilon} = \frac{10^{-2}}{2\pi \epsilon_0 \epsilon_r} = \frac{10^{-2}}{2\pi \times (10^{-9}/36\pi) \times 4} = \frac{10^{-2} \times 18}{10^{-9} \times 4} = 4.5 \times 10^7~\text{Hz} = 45~\text{MHz}$.