L10 (i) For a medium of relative permittivity \(\epsilon_{rel}\), and relative permeability \(\mu_{rel}\):
(a) write the expression for the speed of light, c;
(b) Define the index of refraction, n, in a material.
[4 marks]
[2 marks]
(ii) The speed of light in water is 1.128 larger than the speed of light in glass.
Considering that the relative magnetic permeabilities of glass and of water
are \(\mu_{rel} \approx 1\) and that the index of refraction of glass is \(n_g = 1.5\), determine:
(a) the speed of electromagnetic wave in water;
[5 marks]
(b) the value of water permittivity;
[5 marks]
(c) the impedance value for water,
[5 marks]
(d) The electric field of an electromagnetic wave in water is 1V/m.
Calculate the amplitude of the magnetic field, H in water.
[3 marks]
(iii) Regarding the transfer of energy by an electromagnetic wave:
(a) Define the Poynting vector;
[2 marks]
(b) Place the Poynting vector in a sketch together with the electric field,
magnetic field and the wavevector in free space;
[2 marks]
(c) Using the modulus of the Poynting vector, evaluate the power
transferred per area in water for the case at (ii) (d).
[2 marks]
(iv) Regarding the two material equations parts of Maxwell equations:
(a) write them in vectorial form and explain what are the other vector
quantities apart from vectors E, D, B, H involved;
[8 marks]
(b) Calculate the values of electric and magnetic susceptibilities for
water.
[2 marks]
[\(\epsilon_0 = 8.856 \cdot 10^{-12} F/m\), \(\mu_0 = 4 \cdot \pi \cdot 10^{-7} H/m\)]
