Ampere's Law and Displacement Current

Practice Questions:

Question 1: 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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Question 2: moderate

Which of the following conclusion can be drawn if an electromagnetic wave satisfies the Ampere’s law for vacuum?

1. \(\mu_0 \varepsilon_0 = \frac{B_0}{E_0 c}\)

2. \(c = \frac{B_0}{E_0}\)

3. \(\oint \vec{E} \cdot d\vec{l} = -\frac{d\phi_B}{dt}\)

4. Both (1) and (2)

View Answer

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.

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