Electromagnetic Waves

Practice Questions:

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

1. 3

2. 2

3. \(\sqrt{2}\)

4. \(\sqrt{3}\)

View Answer

The refractive index is given by \(n = \frac{c}{v} = \sqrt{\frac{\varepsilon \mu}{\varepsilon_0 \mu_0}} = \sqrt{2 times 1.5} = \sqrt{3}\).

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Question 2: moderate

To 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

1. 200 V/s

2. 400 V/s

3. 800 V/s

4. 500 V/s

View Answer

Since displacement current is given by \(I_d = C \frac{dV}{dt}\), we find \(\frac{dV}{dt} = \frac{I_d}{C} = \frac{2 \times 10^{-3} \text{A}}{4 \times 10^{-6} \text{F}} = 500 \text{V/s}\).

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