(a) Identify the part of the electromagnetic spectrum used in (i) radar and (ii) eye surgery. Write their frequency range.
(b) Prove that the average energy density of the oscillating electric field is equal to that of the oscillating magnetic field.

(a)(i) Radar—Microwaves are used in radar. The frequency range is from Microwaves: Frequency range (10¹⁰ to 10¹² Hz)
(ii) Eye Surgery — Infrared waves are used. The frequency range is from Ultraviolet rays: Frequency
range (10¹⁵ to 10¹⁷ Hz)
Energy density in oscillating electric field is
${\mathrm{u}}_{\mathrm{E}}=\frac{1}{2}{\mathrm{\epsilon }}_0{\mathrm{E}}^2$
Energy density in oscillating magnetic field is- ${\mathrm{u}}_{\mathrm{B}}=\frac{1}{\left(2{\mathrm{\mu }}_0\right)}{\mathrm{B}}^2$
We know, E=c B
And   $\mathrm{c}=\frac{1}{\sqrt{{\mathrm{\mu }}_0{\mathrm{\epsilon }}_0}}$
So,  ${\mathrm{u}}_{\mathrm{E}}=\frac{1}{2}{\mathrm{\epsilon }}_0(\mathrm{cB}{)}^2=\frac{1}{2}{\mathrm{\epsilon }}_0\frac{1}{{\mathrm{\mu }}_0{\mathrm{\epsilon }}_0}\times {\mathrm{B}}^2$
$=\frac{1}{\left(2{\mathrm{\mu }}_0\right)}{\mathrm{B}}^2$
So,   u_E=u_B