Question

If $E=1kV/m\left(rms\right)$ and the frequency is 10 MHz. then the average power dissipated per cubic meter in a dielectric medium with relative permittivity of 4 and a loss tangent of ${10}^{-3}$ is __________ $W/m^2$

• A. 6.42
• B. 2.22
• C. 8.25
• D. 1.02

Answer 1

The correct option is B 2.22

$\tan \theta =\frac{\sigma }{\omega \epsilon }$

$\sigma =\omega \epsilon \tan \theta$

$\sigma =2\pi \times 10\times {10}^6\times 8.85\times {10}^{-12}\times 4\times {10}^{-3}$

$\sigma =2.22\mu \mho /m$

Power dissipated per unit volume

$P_{\text{diss}}=\sigma E^2$

$=2.22\times {10}^{-6}\times {10}^6$

$=2.22W/m^3$