Question 1:
moderate\(\varepsilon_0\) and \(\mu_0\) are the electric permittivity and magnetic permeability of free space respectively. If the corresponding quantities of a medium are \(2\varepsilon_0\) and \(1.5\mu_0\) respectively, the refractive index of the medium will nearly be
The refractive index is given by \(n = \frac{c}{v} = \sqrt{\frac{\varepsilon \mu}{\varepsilon_0 \mu_0}} = \sqrt{2 times 1.5} = \sqrt{3}\).
Question 2:
moderateTo produce an instantaneous displacement current of 2 mA in the space between the parallel plates of a capacitor of capacitance \(4 \mu\text{F}\), the rate of change of applied variable potential difference \(\left(\frac{dV}{dt}\right)\) must be
Since displacement current is given by \(I_d = C \frac{dV}{dt}\), we find \(\frac{dV}{dt} = \frac{I_d}{C} = \frac{2 \times 10^{-3} \text{A}}{4 \times 10^{-6} \text{F}} = 500 \text{V/s}\).
Question 3:
moderateWhich of the following conclusion can be drawn if an electromagnetic wave satisfies the Ampere’s law for vacuum?
For an EM wave in vacuum, \(c = \frac{E_0}{B_0}\) and \(c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}\). Substituting \(\frac{B_0}{E_0} = \frac{1}{c}\) into \(mu_0 \varepsilon_0 = \frac{B_0}{E_0 c}\) gives \(mu_0 \varepsilon_0 = \frac{1}{c^2}\), which is true.