JEE Electromagnetic Waves PYQs with Video Solutions PDF

An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, $$\sigma$$ = 10mho/m. The ratio of maximum conduction current density to maximum displacement current
density is ___________.
[Take $$\frac{1}{4\pi \epsilon_{0}} = 9 \times 10^{9} Nm^{2}/C^{2}$$]

The electric field in a plan a electromagnetic wave is given by :
$$E_{y}=69\sin[0.6\times10^{3}x-1.8\times10^{11}t]V/m$$
The expression for magneticfield associated with this electromagnetic wave is ___ T.

A laser beam has intensity of $$4.0 \times 10^{14} W/m^{2}.$$ The amplitude of magnetic field associated with beam is____________T. (Take $$\epsilon_{0}= 8.85 \times 10^{-12} C^{2}/Nm^{2}$$ and $$c= 3 \times 10^{8} m/s$$ )

The equation of the electric field of an electromagnetic wave propagating through free space is given
by: E=$$\sqrt{377}$$ $$\sin(6.27\times10^{3}t-2.09\times 10^{-5}x)N/C$$
The average power of the electromagnetic wave is $$\left(\frac{1}{\alpha}\right)W/m^{2}$$. The value of $$\alpha$$ is______
$$\left(Take \sqrt{\frac{\mu_{\circ}}{\epsilon_{\circ}}}=377 in SI units \right)$$

The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by,

$$ E_{y}=20 \sin (3\times 10^{6}x - 4.5\times 10^{14}t)V/m $$
(where $$x, t$$ and other values have S.I. units). The dielectric constant of the medium iS_________
(speed oflight in free space is $$ 3\times 10^{8} m/s $$)

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

The electric field of an electromagnetic wave travelling through a medimn is given by $$\overrightarrow{E}(x,t)=25\sin(2.0\times 10^{15}t-10^{7}x)\widehat{n}$$ then the refractive index of the medium is______.
(All given measurement are in SI uits)

The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant $$k = 3$$ and permeability of $$ \mu = 2 \mu_{0}$$, is
($$\mu_{0}$$ = permeability of vacuum)

A plane electromagnetic wave is moving in free space with velocity $$c=3\times 10^{8} m/s$$ and its eleclric field is given as $$\overrightarrow{E}=54\sin (kz-\omega t)\widehat{j} V/m$$, where $$\widehat{j}$$ is the unit vector along y-axis. The magnetic field vector $$\overrightarrow{B}$$ of the wave is :

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

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 $$E_{y}=9.3Vm^{-1}$$. Then, the magnetic field vector of the wave at that point is

Arrange the following in the ascending order of wavelength $$ (\lambda) $$ : (A) Microwaves $$ (\lambda_1) $$(B) Ultraviolet rays $$ (\lambda_2) $$ (C) Infrared rays $$ (\lambda_3) $$ (D) X-rays $$ (\lambda_4) $$ Choose the most appropriate answer from the options given below

Due to presence of an em-wave whose electric component is given by $$E = 100\sin(\omega t - kx)NC^{-1}$$, a cylinder of length 200 cm holds certain amount of em-energy inside it. If another cylinder of same length but half diameter than previous one holds same amount of em-energy, the magnitude of the electric field of the corresponding em-wave should be modified as

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Electromagnetic waves carry energy but not momentum. Reason (R): Mass of a photon is zero. In the light of the above statements, choose the most appropriate answer from the options given below :

The electric field of an electromagnetic wave in free space is
$$\vec{E} = 57 \cos \left[ 7.5 \times 10^{6} t - 5 \times 10^{-3} (3x + 4y) \right] (4\hat{i} - 3\hat{j}) N / C$$. The associated magnetic field in Tesla is

The magnetic field of an E.M. wave is given by $$\vec{B} = \left(\frac{\sqrt{3}}{2}\,\hat{i} + \frac{1}{2}\,\hat{j}\right) 30 \sin\left[\omega \left(t - \frac{z}{c}\right)\right] \; \text{(S.I. Units)}.$$ corresponding electric field in S.I. units is :

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$$^{-1}$$. The rms value of conduction current in the circuit and displacement current in the capacitor respectively are :

If frequency of electromagnetic wave is 60 MHz and it travels in air along z direction then the corresponding electric and magnetic field vectors will be mutually perpendicular to each other and the wavelength of the wave in m is:

A plane electromagnetic wave propagating in $$x$$-direction is described by $$E_y = (200 \text{ V m}^{-1}) \sin[1.5 \times 10^7 t - 0.05x]$$. The intensity of the wave is : (Use $$\epsilon_0 = 8.85 \times 10^{-12} \text{ C}^2 \text{ N}^{-1} \text{ m}^{-2}$$)

An object is placed in a medium of refractive index 3. An electromagnetic wave of intensity $$6 \times 10^8$$ W m$$^{-2}$$ falls normally on the object and it is absorbed completely. The radiation pressure on the object would be (speed of light in free space = $$3 \times 10^8$$ m s$$^{-1}$$) :

A plane electromagnetic wave of frequency $$35$$ MHz travels in free space along the $$X$$-direction. At a particular point (in space and time) $$\vec{E} = 9.6\hat{j}$$ V m$$^{-1}$$. The value of magnetic field at this point is:

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 :

If the total energy transferred to a surface in time $$t$$ is $$6.48 \times 10^5$$ J, then the magnitude of the total momentum delivered to this surface for complete absorption will be:

In a plane EM wave, the electric field oscillates sinusoidally at a frequency of $$5 \times 10^{10}$$ Hz and an amplitude of $$50 \text{ V m}^{-1}$$. The total average energy density of the electromagnetic field of the wave is : [Use $$\varepsilon_0 = 8.85 \times 10^{-12} \text{ C}^2 \text{N}^{-1}\text{m}^{-2}$$]

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:

Match List I with List II:

Choose the correct answer from the options given below:

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:

Match List-I with List-II :

The density and breaking stress of a wire are $$6 \times 10^4 \text{ kg/m}^3$$ and $$1.2 \times 10^8 \text{ N/m}^2$$ respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is $$\frac{1}{3}^{rd}$$ of the value on the surface of earth. The maximum length of the wire with breaking is ______ m (take, $$g = 10 \text{ m/s}^2$$).

Average force exerted on a non-reflecting surface at normal incidence is $$2.4 \times 10^{-4} \text{ N}$$. If $$360 \text{ W/cm}^2$$ is the light energy flux during span of 1 hour 30 minutes, Then the area of the surface is: