Maxwell's equations and Concept of displacement current PYQs: JEE Mains Physics

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1. 1. A displacement current of \(4.0\) A can be set up in the space between two parallel plates of \(6\) \(\mu\)F capacitor. The rate of change of potential difference across the plates of the capacitor is nearly \(\alpha \times 10^6\) V/s. The value of \(\alpha\) is __________. 2026 Easy
2. 2. An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, \(\sigma=10 mho / m\). The ratio of maximum conducting current density to maximum displacement current density is _________ .
   \(\left[\right.\) Take \(\left.\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 Nm ^2 / C ^2\right]\) 2026 Hard
3. 3. Match List-I with List-II.

   List-I (Relation)		List-II (Law)
   A.	\(\oint \overrightarrow{ E } \cdot \overrightarrow{ d } l =-\frac{ d }{ dt } \oint \overrightarrow{ B } \cdot \overrightarrow{ d a}\)	I.	Ampere's circuital law.
   B.	\(\oint\) B. \(\vec{d} l=\mu_0\left(1+\epsilon_0 \frac{d \phi_E}{d t}\right)\)	II.	Faraday's laws of electromagnetic induction.
   C.	\(\oint \overrightarrow{ E } . \overrightarrow{ d a}=\frac{1}{\epsilon_0} \int \rho dv\)	III.	Ampere-Maxwell law
   D.	\(\oint \overrightarrow{ B } \cdot \overrightarrow{ d } l =\mu_0 I\)	IV.	Gauss's law of electrostatics

   Choose the correct answer from the options given below : 2026 Easy
4. 4. A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A . If the rate of change of potential difference between the plates is \(7 \times 10^8 \mathrm{~V} / \mathrm{s}\) then the integer value of the distance between the parallel plates is \(\left(\right.\) Take, \(\left.\epsilon_0=9 \times 10^{-12} \frac{\mathrm{~F}}{\mathrm{~m}}, \pi=\frac{22}{7}\right)\) ________ \(\mu \mathrm{m}\). 2025 Medium
5. 5. A time varying potential difference is applied between the plates of a parallel plate capacitor of capacitance \(2.5 \mu \mathrm{~F}\). The dielectric constant of the medium between the capacitor plates is 1 . It produces an instantaneous displacement current of 0.25 mA in the intervening space between the capacitor plates, the magnitude of the rate of change of the potential difference will be _____ \(\mathrm{Vs}^{-1}\). 2025 Hard
6. 6. An alternating voltage of amplitude \(40 \mathrm{~V}\) and frequency \(4 \mathrm{kHz}\) is applied directly across the capacitor of \(12 \mu \mathrm{F}\). The maximum displacement current between the plates of the capacitor is nearly _______. 2024 Hard
7. 7. Maatch Liat \(I\) List \(II\) Chose the correct answer from the options given below
   2024 Hard
8. 8. Match List\(-I\) with List\(-II\).

   List\(-I\)	List\(-II\)
   \(A\). Gauss's Law in Electrostatics	\(I\). \(\oint \vec{E} \cdot d \vec{l}=-\frac{d \phi_B}{d t}\)
   \(B\). Faraday's Law	\(II\). \(\oint \overrightarrow{ B } \cdot d \overrightarrow{ A }=0\)
   \(C\). Gauss's Law in Magnetism	\(III\). \(\oint \vec{B} \cdot d \vec{l}=\mu_0 i_C+\mu_0 \in_0 \frac{d \phi_E}{d t}\)
   \(D\). Ampere-Maxwell Law	\(IV\). \(\oint \overrightarrow{ E } \cdot d \overrightarrow{ s }=\frac{ q }{\epsilon_0}\)

   Choose the correct answer from the options given below: 2024 Medium
9. 9. Which of the following Maxwell's equations is valid for time varying conditions but not valid for static conditions 2023 Medium
10. 10. Seawater at a frequency \(f =9 \times 10^{2} \,Hz ,\) has permittivity \(\varepsilon=80\, \varepsilon_{0}\) and resistivity \(\rho=0.25\, \Omega m.\) Imagine a parallel plate capacitor is immersed in seawater and is driven by an alternating voltage source \(V ( t )= V _{0} \sin (2 \pi ft ) .\) Then the conduction current density becomes \(10^{x}\) times the displacement current density after time \(t =\frac{1}{800} \,s\). The value of \(x\) is ......... .
    \(\left(\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} Nm ^{2} C ^{-2}\right)\) 2021 Hard
11. 11. A plane polarized monochromatic \(EM\) wave is travelling a vacuum along \(z\) direction such that at \(t\, = t_1\) it is found that the electric field is zero at a spatial point \(z_1\) . The next zero that occurs in its neighbourhood is at \(z_2\). The frequency of the electromagnetic wave is: 2018 Hard
12. 12. To establish an instantaneous current of \(2\,A\) through a \(1\,\mu F\) capacitor ; the potential difference across the capacitor plates should be changed at the rate of 2013 Medium

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