Electromagnetic waves are produced by

An electromagnetic wave of frequency $100 \text{ MHz}$ propagates through a medium of conductivity $\sigma = 10 \text{ mho/m}$. The ratio of maximum conducting current density to maximum displacement current density is . . . . . . . $\left[ \text{Take } \frac{1}{4 \pi \epsilon_0} = 9 \times 10^9 \text{ Nm}^2/\text{C}^2 \right]$

Suppose that the electric flux inside a parallel plate capacitor changes at a rate of $7 \times 10^{14} \text{ V} \cdot \text{m/s}$. If the area of the plates is $1 \text{ m}^2$,calculate the magnetic field $B$ at a distance $r = 0.1 \text{ m}$ from the axis of the capacitor. (Given: $\varepsilon_0 = 8.85 \times 10^{-12} \text{ F/m}$,$\mu_0 = 4\pi \times 10^{-7} \text{ T} \cdot \text{m/A}$)

$A$ long straight cable of length $l$ is placed symmetrically along $z-$ axis and has radius $a (a << l)$. The cable consists of a thin wire and a co-axial conducting tube. An alternating current $I(t) = I_0 \sin(2\pi \nu t)$ flows down the central thin wire and returns along the co-axial conducting tube. The induced electric field at a distance $s$ from the wire inside the cable is $\vec{E}(s,t) = \mu_0 I_0 \nu \cos(2\pi \nu t) \ln(s/a) \hat{k}$.
$(i)$ Calculate the displacement current density inside the cable.
$(ii)$ Integrate the displacement current density across the cross-section of the cable to find the total displacement current $I_d$.
$(iii)$ Compare the conduction current $I_0$ with the displacement current $I_d$.

The displacement current of $4.425 \,\mu A$ is developed in the space between the plates of a parallel plate capacitor when the voltage is changing at a rate of $10^{6} \,V s^{-1}$. The area of each plate of the capacitor is $40 \,cm^{2}$. The distance between the plates of the capacitor is $x \times 10^{-3} \,m$. The value of $x$ is ................ (Permittivity of free space,$\varepsilon_{0} = 8.85 \times 10^{-12} \,C^{2} N^{-1} m^{-2}$)

Which scientist first time produced electromagnetic waves in laboratory?