Q 11 :    

A parallel plate capacitor has a capacitance $C=200$ $pF$. It is connected to 230 V AC supply with an angular frequency 300 rad/s. The RMS value of conduction current in the circuit and displacement current in the capacitor respectively are            [2024]

• $1.38\mu A$ and $1.38\mu A$

   

• $14.3\mu A$ and $143\mu A$

   

• $13.8\mu A$ and $138\mu A$

   

• $13.8\mu A$ and $13.8\mu A$

   

Q 12 :    

The electric field in an electromagnetic wave is given by $\overrightarrow{E}=\hat{i} 40\cos \omega (t-\frac{{\displaystyle z}}{{\displaystyle c}}){\text{ NC}}^{-1}$.  The magnetic field induction of this wave is (in SI unit):      [2024]

• $\overrightarrow{B}=\hat{j} 40\cos \omega (t-\frac{{\displaystyle z}}{{\displaystyle c}})$

   

• $\overrightarrow{B}=\hat{k}\frac{40}{c}\cos \omega (t-\frac{{\displaystyle z}}{{\displaystyle c}})$

   

• $\overrightarrow{B}=\hat{i}\frac{40}{c}\cos \omega (t-\frac{{\displaystyle z}}{{\displaystyle c}})$

   

• $\overrightarrow{B}=\hat{j}\frac{40}{c}\cos \omega (t-\frac{{\displaystyle z}}{{\displaystyle c}})$

   

Q 13 :    

The electric field of an electromagnetic wave in free space is

$\overrightarrow{E}=57 \cos [7.5\times {10}^{6}t–5\times {10}^{–3}(3x+4y\left)\right](4\hat{i}–3\hat{j})\mathrm{N}/\mathrm{C}$

The associated magnetic field in Tesla is:          [2025]

• $\overrightarrow{B}=\frac{57}{3\times {10}^8} \cos [7.5\times {10}^{6}t–5\times {10}^{–3}(3x+4y\left)\right]\left(5\hat{k}\right)$

   

• $\overrightarrow{B}=\frac{57}{3\times {10}^8} \cos [7.5\times {10}^{6}t–5\times {10}^{–3}(3x+4y\left)\right]\left(\hat{k}\right)$

   

• $\overrightarrow{B}=–\frac{57}{3\times {10}^8} \cos [7.5\times {10}^{6}t–5\times {10}^{–3}(3x+4y\left)\right]\left(5\hat{k}\right)$

   

• $\overrightarrow{B}=–\frac{57}{3\times {10}^8} \cos [7.5\times {10}^{6}t–5\times {10}^{–3}(3x+4y\left)\right]\left(\hat{k}\right)$

   

Q 14 :    

A plane electromagnetic wave of frequency 20 MHz travels in free space along the +x direction. At a particular point in space and time, the electric field vector of the wave is $E_y=9.3 {\mathrm{Vm}}^{–1}$. Then, the magnetic field vector of the wave at the point is          [2025]

• $B_z=9.3\times {10}^{–8}\mathrm{T}$

   

• $B_z=1.55\times {10}^{–8}\mathrm{T}$

   

• $B_z=6.2\times {10}^{–8}\mathrm{T}$

   

• $B_z=3.1\times {10}^{–8}\mathrm{T}$

   

Q 15 :    

The magnetic field of an E.M. wave is given by

$\overrightarrow{B}=(\frac{\sqrt{3}}{2}\hat{i}+\frac{1}{2}\hat{j})30\sin \left[\omega \right(t–\frac{z}{c}\left)\right]$ (SI Units)

The corresponding electric field in S.I. units is:          [2025]

• $\overrightarrow{E}=(\frac{1}{2}\hat{i}–\frac{\sqrt{3}}{2}\hat{j})30c \sin \left[\omega \right(t–\frac{z}{c}\left)\right]$

   

• $\overrightarrow{E}=(\frac{3}{4}\hat{i}+\frac{1}{4}\hat{j})30c \cos \left[\omega \right(t–\frac{z}{c}\left)\right]$

   

• $\overrightarrow{E}=(\frac{1}{2}\hat{i}+\frac{\sqrt{3}}{2}\hat{j})30c \sin \left[\omega \right(t+\frac{z}{c}\left)\right]$

   

• $\overrightarrow{E}=(\frac{\sqrt{3}}{2}\hat{i}–\frac{1}{2}\hat{j})30c \sin \left[\omega \right(t+\frac{z}{c}\left)\right]$

   

Q 16 :    

A plane electromagnetic wave propagates along the +x direction in free space. The components of the electric field, $\overrightarrow{E}$ and magnetic field, $\overrightarrow{B}$ vectors associated with the wave in Cartesian frame are:          [2025]

• $E_y, B_x$

   

• $E_y, B_z$

   

• $E_x, B_y$

   

• $E_z, B_y$

   

Q 17 :    

If ${\epsilon }_0$ denotes the permittivity of free space and ${\Phi }_E$ is the flux of the electric field through the area bounded by the closed surface, then dimension of $\left({\epsilon }_0\frac{d{\varphi }_E}{dt}\right)$ are that of:          [2025]

• Electric field

   

• Electric potential

   

• Electric charge

   

• Electric current

   

Q 18 :    

A parallel plate capacitor of area A = 16 ${\mathrm{cm}}^2$ and separation between the plates 10 cm, is charged by a DC current. Consider a hypothetical plane surface of area $A_0=3.2 {\mathrm{cm}}^2$ inside the capacitor and parallel to the plates. At an instant, the current through the circuit is 6 A. At the same instant the displacement current through $A_0$ is _______ mA.          [2025]

Q 19 :    

A time varying potential difference is applied between the plates of a parallel plate capacitor of capacitance 2.5 $\mu$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 _______ ${\mathrm{Vs}}^{–1}$.