Q2. A cellphone signal at 900 MHz propagates in the grey matter of the
brain which has constitutive parameters $\epsilon_r$ = 50, $\sigma$ = 0.8 S/m, and
$\mu_r$ = 1.
(i) Determine the loss tangent tan $\delta$, the loss angle $\delta$, the
propagation constant $\gamma$, the attenuation constant $\alpha$, the phase
constant $\beta$, the skin depth $\delta$, the wavelength $\lambda$ and the phase
velocity $u_p$.
(ii) Find the distance inside the brain at which the magnitude of the
fields is 10% of that at the surface. State any assumption made.
Ans: tan $\delta$ = 0.32, $\delta$ = 17.74$^\circ$, $\gamma$ = 21.34 Np/m + j134.95 rad/m,
$\alpha$ = 21.34 Np/m, $\beta$ = 134.95 rad/m, $\delta$ = 0.0469 m,
$\lambda$ = 0.0466 m, $u_p$ = 4.19 × 10$^7$ m/s, 0.108 m