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A plane electromagnetic wave propagating in \( x \)-direction is described by \( E_{y} = (200 \, \mathrm{V \, m^{-1}})\sin[1.5 \times 10^{7} t - 0.05 \, x] \);
The intensity of the wave is : (Use \( \varepsilon_{0} = 8.85 \times 10^{-12} \, \mathrm{C^{2} \, N^{-1} \, m^{-2}} \) )

If the total energy transferred to a surface in time \( t \) is \( 6.48\times10^{5}\, \text{J} \), then the magnitude of the total momentum delivered to this surface for complete absorption will be:

Match List I with List II:

Choose the correct answer from the options given below:

A parallel plate capacitor has a capacitance \( C = 200 \, \text{pF} \). It is connected to \( 230 \, \text{V} \) ac supply with an angular frequency \( 300 \, \text{rad}/\text{s} \). The rms value of conduction current in the circuit and displacement current in the capacitor respectively are:

A plane electromagnetic wave of frequency \( 35 \, \text{MHz} \) travels in free space along the X-direction. At a particular point (in space and time) \( \vec{E} = 9.6 \, \hat{j} \, \text{V/m} \). The value of magnetic field at this point is:

In a plane EM wave, the electric field oscillates sinusoidally at a frequency of \( 5 \times 10^{10} \, \text{Hz} \) and an amplitude of \( 50 \, \text{V m}^{-1} \). The total average energy density of the electromagnetic field of the wave is:
[Use \( \varepsilon_0 = 8.58 \times 10^{-12} \, \text{C}^2 /\text{N m}^2 \)]

The electric field of an electromagnetic wave in free space is represented as \( \vec{E} = E_{0} \cos(\omega t - kz) \, \hat{i} \). The corresponding magnetic induction vector will be:

An alternating voltage of amplitude \( 40 \, \text{V} \) and frequency \( 4 \, \text{kHz} \) is applied directly across the capacitor of \( 12 \, \mu \text{F} \). The maximum displacement current between the plates of the capacitor is nearly:

The electric field in an electromagnetic wave is given by \( \vec{E} = \hat{\imath} \, 40 \cos \omega \!\left( t - \frac{z}{c} \right) \, \text{N C}^{-1} \). The magnetic field induction of this wave is (in SI unit):

A plane EM wave is propagating along \( x \) direction. It has a wavelength of \( 4 \, \text{mm} \). If electric field is in \( y \) direction with the maximum magnitude of \( 60 \, \text{V m}^{-1} \), the equation for magnetic field is:

Arrange the following in the ascending order of wavelength:
A. Gamma rays \( (\lambda_1) \) B. x – rays \( (\lambda_2) \)
C. Infrared waves \( (\lambda_3) \) D. Microwaves \( (\lambda_4) \)
Choose the most appropriate answer from the options given below:

Given below are two statements:
Statement I: Electromagnetic waves carry energy as they travel through space and this energy is equally shared by the electric and magnetic fields.
Statement II: When electromagnetic waves strike a surface, a pressure is exerted on the surface.
In the light of the above statements, choose the most appropriate answer from the options given below:

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JEE Main 2024 4th April Morning Shift

The electric field in an electromagnetic wave is given by \( \vec{E} = \hat{\imath} \, 40 \cos \omega \!\left( t - \frac{z}{c} \right) \, \text{N C}^{-1} \). The magnetic field induction of this wave is (in SI unit):