Q.(a)

(a) Electromagnetic waves are transverse, self-propagating oscillations of E and B fields travelling at speed $c$; here the medium's refractive index computes to about 2.37. (b) A transistor in common-emitter configuration amplifies a small base-current signal into a large, phase-inverted collector-voltage output. Both alternatives answered below.

(a)(i) Properties of electromagnetic waves

• Transverse nature: the electric field $\vec E$ and magnetic field $\vec B$ oscillate perpendicular to each other, and both are perpendicular to the direction of wave propagation.
• Mutual phase: $\vec E$ and $\vec B$ oscillate in phase -- they reach their maximum and zero values simultaneously.
• Speed: in free space/vacuum, all electromagnetic waves travel at the same speed, $c=\dfrac{1}{\sqrt{\mu_0\varepsilon_0}}\approx3\times10^8\,m/s$; in a medium, the speed is $v=\dfrac{1}{\sqrt{\mu\varepsilon}}=\dfrac{c}{n}$ where $n$ is the refractive index.
• No medium required: unlike mechanical waves, EM waves can propagate through vacuum (empty space); they do not need any material medium.
• Amplitude ratio: the ratio of the peak electric and magnetic field magnitudes equals the speed of light, $E_0/B_0=c$.
• Energy and momentum: EM waves transport energy (described by the Poynting vector) and momentum, and hence exert radiation pressure on absorbing/reflecting surfaces.
• Self-sustaining: once generated (e.g., by an accelerating charge), the wave propagates on its own, each changing field regenerating the other via Maxwell's displacement-current mechanism, with no need for charges to keep oscillating along the path.
• Wide spectrum: EM waves span an enormous range of frequencies/wavelengths (radio, microwave, infrared, visible, UV, X-ray, gamma ray), all sharing the above properties but differing in production/detection method and interaction with matter.

(a)(ii) Refractive index from $\mu_r$ and $\varepsilon_r$

Formula. The refractive index of a medium relative to vacuum is

$n = \sqrt{\mu_r\,\varepsilon_r}$

where $\mu_r$ is the relative magnetic permeability and $\varepsilon_r$ is the relative electrical permittivity (dielectric constant) of the medium.

Given: $\mu_r = 2.5$, $\varepsilon_r = 2.25$.

Substitution:

$n = \sqrt{2.5\times2.25} = \sqrt{5.625}$

$n \approx 2.372$

(b) Transistor as an amplifier (common-emitter configuration)

1. Circuit description. The transistor is connected in the common-emitter (CE) mode: the input AC signal is applied (via a coupling capacitor, to block DC) between base and emitter; a voltage-divider (or base-resistor) network sets the correct DC bias so the transistor operates in the active region; the output is taken across a load resistor $R_C$ connected between the collector and the supply $V_{CC}$, coupled out via another capacitor.

Schematically:

                Vcc
                 |
                R_C
                 |
    input --[C]--o-- Base   Collector --o-- output (across R_C, via coupling cap)
                    (NPN transistor, CE mode)
                       Emitter
                          |
                        ground (with emitter resistor + bypass cap, typically)

Base biased by an R1-R2 voltage-divider network to set the operating point.

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