Q.3) Superposition principle
(25 marks)
Consider a general inhomogeneous medium. Show that if ($E_1, H_1$) and ($E_2, H_2$) are the phasor
solutions of Maxwell's equations in the frequency-domain at frequencies $\omega_1$ and $\omega_2$ respectively,
the fields ($a_1E_1e^{j\omega_1t} + a_2E_2e^{j\omega_2t} + c.c., a_1H_1e^{j\omega_1t} + a_2H_2e^{j\omega_2t} + c.c.$) satisfy the
Maxwell's equations in the time-domain for arbitrary real numbers $a_1$ and $a_2$. Here c.c. stands for
complex conjugate. Generalize this result to show that for any arbitrary real valued function a($\omega$),
($\int dw \ a(\omega) E_\omega(r)e^{j\omega t} + c.c., \int dw \ a(\omega)H_\omega(r)e^{j\omega t} + c.c.$) solves the time-domain
Maxwell's equations, where ($E_\omega(r), H_\omega(r)$) is the phasor solution at frequency $\omega$.
