Electromagnetic waves Questions and Answers

he electric field in an electromagnetic wave is E 10 sin wt kz i volt The corresponding magnetic field associated is 104 3x10 OB B sin ot kz i Tesla 104 3 x 108 OB 104 B sin ot kz 1 Tesla 3 x 10 10 sintot kzi Tesla sintot kzk Tesla 103

An em wave is propagating in a medium with a velocity V V The instantaneous oscillating electric field of this em wave is along y axis Then the direction of oscillating magnetic field of the em wave will be along A y direction B z direction C x direction D z direction

The electric field in an electromagnetic wave is E 10 sin wt kz i volt The corresponding magnetic m field associated is OB OB OB 104 3x108 sin ot kz i Tesla 104 3 x 108 104 3 x 108 sin ot kz 1 Tesla sin ot kz j Tesla

Consider a circular disc of radius a in the xy plane centered on the origin and containing a surface charge density o r 8 arcose where is the angle made by the position vector with a fixed diameter chosen as x axis Find the dipole moment of the charge distribution

Consider a system of three charges 2q charge at the origin q at I and another charge g at 1 Find the dipole moment p of the system What is the magnitude of p if 1 and angle between I and I is 9

A CO a sir oidal wave moving in the x direction y x t A sin t A wall located at x L reflects this wave Mark the CORRECT statement s B sin 7 x x 2L 1 7 x C If the wall is a fixed end the resultant wave is 2A sin cos t If the wall is a free end the resultant wave is 2A cos 2 sin t 4 If the wall is a fixed end the expression for reflected wave is A sin If the wall is a free end the expression for reflected waves is A sin

A positive charge is passing through an electromagnetic field in which E B are direct towards y axis z axis respectively If a charge particle passes through the region undeviat then its velocity is are represented by here a b c are constant AX Ei a E C v i ci B Ei bk B E D v

45 Charge is uniformly distributed with volume charge density p in a spherical volume of radius R A cavity of radius r is made in the charge distribution such that the centre of the cavity is at distance a from the centre of the charge distribution then the electric field in the cavity is X f 1 Zero 2 Non zero and non uniform 3 Non zero uniform and equal to 4 Non zero uniform and equal to Pa 280 360 1 0

In the spectrum of light of a luminous heavenly body the wavelength of a spectral line is measured to be 4747 while actual wavelength of the line is 4700 The relative velocity of the heavenly body with respect to earth will be velocity of light is 3 108 m s 1 3 x 105 m s towards earth 2 3 x 105 m s away from earth 3 3 x 106 m s towards earth 4 3 x 106 m s away from earth

an I WA 9 X q XX Bx X X harge a projected perpendicular to the electric hen moves through the magnetic field 9x X X XE X arge is released form rest in crossed B and E E arge is projected perpendicular to E in a E and B B 9 ge is projected at a non zero angel 8 90 magnetic induction Column II A B m C D C

A plane electromagnetic wave is propagating along the direction 2 1 Bo 2 direction The correct from of the magnetic field of wave would be here B is an appropriate constant JEE Main 2020 January 0 with its polarization along the 1 2 cos a cos cot k 3 Bo 2 B cos tot k Bo 2 443239 2 cos oot k i

Example A particle of rest mass m moving with speed v w r t laboratory frame collides with another particle of rest mass m kept initially at rest After collision the two particles coalasce to form a new entity Calculate the speed and rest mass of final entity

The plots of intensity v s wavelength for three black bodies at temperatures T T T respectively Their temperature are such that Decreasing order 3 I a T T T 3 bib T T T c T T T wd T T T 3 T T T zes ai 8 to PrepOnline NEET Select the correct option Anonymous Quiz O192 7 58 PM

Example In a rocket light is used as propellent Initially rocket is at rest and its rest mass is m It attains some speed by emission of light in opposite direction Ifm is the final rest mass of rocket find the speed attained by rocket

PQRS is a square of side lo A B C and D are four long current carrying wires kept perpendicular to the plane of paper as shown in the figure PA QB RC SD The magnitude of current in the wires A B C and D are io 2i0 8i0 and 4io respectively the direction of current are shown It is given Q that B de A 9 0 Tesla meter and P S SBB de R S D A BA and BB are the magnetic fields due to the wires A and B respectively The magnitude of io is lo 5 5 0 Tesla meter where B R

A log of mass m is pulled at a constant velocity and with a force F by means of a rope of length 7 The distance between the end of the rope and the ground is h as shown Find the co efficient of friction between the log and the ground 1 h

19 A flexible wire bent in the form of a circle is placed in a uniform magnetic field perpendicular to the plane of the circle The radius r of circle changes with time t as shown in the figure The graph of magnitude of induced emf jel versus time in the circle is represented by 1 a Educational Semi b lel 2 kla H 14 lel 2 4 2 lel d lel t 1 2 t

If a source of power 4kW produces 1020 photons second the radiation belongs to part of the spectrum called Question Type Single Correct Type 1 y rays 2 X rays 3 Ultraviolet rays

A Stretched wire of length 110 cm is divided into three segments whose frequencies are in ratio 1 2 3 Their length must be Question Type Single Correct Type 1 2 3 4 20 cm 30 cm 60 cm 60 cm 30 cm 20 cm 60 cm 20 cm 30 cm 30 cm 60 cm 20 cm Status Unattempted

28 A plane electromagnetic wave of 1 meter wavelength is propagating in 3 Z direction in a infinitely extended lossless medium having constants H 1 and 9 If amplitude of electric field vector is 100 Volt meter then expression for electric field vector is A E 100sin 1800x10 t 67 B E 100sin 900x10 t 6 C E 100sin 600x10 t 6 D E 100sin 300x10 1 2

Example Two particles A and B of mass m and one particle C of mass M are kept on thex axis in the order ABC Particle A is given a velocity vi Consequently there are two collisions both of which are completely inelastic If the net energy loss because of these collisions is of the initial energy the value of Mis ignore frictional losses c 4 m d 2 m

13 At a certain instant in time the electric field of an electromagnetic wave in free space points in the z direction and the magnetic field points in the y direction In what direction is this wave traveling A x direction B x direction C y direction D z direction 4 A certain part of the electromagnetic spectrum ranges from 200 nm to 400 nm What is the lowest frequency associated with this portion of the spectrum A 1 50 x 10 4 Hz B 7 50 x 10 3 Hz C 7 50 x 10 4 Hz D 7 50 x 10 5 Hz

There is spherical symmetric charge distribution around origin The electrostatic potential at a distance from origin 4 Kr 1 is given as V where K is a positive constant The slope of tangent to density vs r graph at r m 2 4 is aK E Then find value of a

For an electromagnetic wave travelling along y axis the electric field component is known to be along SE 31 4k at an instant The direction of magnetic field at this instant is along 1 31 4k 3 41 3k betbenno 2 3 4K 4 41 3k

At a distance of 5 cm and 10 cm outwards from the surface of a uniformly charged solid sphere capacitance 4 R the electric potentials are 100 V and 75 V respectively Choose the corre option s where R is radius of sphere A Potential at its surface is 150 V B Charge on the sphere is 5 3 x 10 C C Electric field on the surface of the sphere is 1500 V m D Electric potential at the centre of the sphere is 225 V

5 A charged particle mass m charge q is moving in a region of uniform magnetic field Bok If at time t 0 the particle is at the origin and has a velocity i uxi u k what is the position vector of the particle at a later time m qBo A 7 B 7 C 7 D 7 2mux qBo 2mux qBo 9 muz qBo k 9 muz qBo 2m Vu u a Ro 9 muz qBo k

ree EM waves of frequencies f c 100Hz 1MHz 10GHz are incident on 3 different jects whose diameters are listed below Estimate to 10 precision the intensity of the lected wave for each case as a fraction of incident intensity All surfaces are 100 reflecti 100 Hz 1 MHz reflected 5 mm ball bearing 300m container ship 13 Mm earth 10GHz

When photon of energy 4 0 eV strikes the surface of a metal A the ejected photoelectrons have maximum kinetic energy TA eV end de Broglie wavelength AA The maximum kinetic energy of photoelectrons liberated from another metal B by photon of energy 4 50 eV is TB TA 1 5 eV If the de Broglie wavelength of these photoelectrons Ag 2 A then the work function of metal B is 1 3eV 2 2eV 3 4eV 4 1 5eV

9 A spherical body of area A and emissivity 0 6 is kept inside a perfectly black body Totalt radiated by the body at temperature Tis A 0 46 AT 10 6 GAT The graph shown in the figure versus 8 0 155 105 D 1 01 10 200 B 0 8 AT D 1 0 AT

If a 24 V m electric field of frequency 4 0 x 1010 Hz oscillates sinusoidally in a plane electromagnetic wave then the total average energy density of the wave is A B 1 0 x 10 8 J m3 0 25 x 10 8 J m C 1 6 x 10 8 J m

1 A cylindrical rod of length 1 64cm and cross sectional radius r 2 cm is placed at a distance 50r from an infrared point source S of power 1 25kW as shown in fig 50r The lateral surface area of the rod is perfectly insulated from the surroundings The cross section A absorbs 80 of the incident energy and has temperature TA in steady state The surface B is radiating energy into space and the wavelength emitted by it with maximum energy density is 100 000 A The temperature of end B and value of TA if conductivity varies with temperature as K T T is Assume that the rate of flow of heat through the rod is steady Wein s constant 0 003mK A 200 K and 500 K B 400 K and 500 K C 300K and 500K D 300K and 400K

Choose the correct statement s GA A longitudinal electric field wave is not possible B A longitudinal magnetic field wave is not possible The electric and magnetic waves are in phase with one another D The electric and magnetic vectors are mutually perpendicular and both are perpendicu the direction of propagation of the electromagnetic wave

In an EM wave propagating along X direction magnetic field oscillates at a frequency of 3 x 10 0 Hz along Y direction and has an amplitude of 10 7 T The expression for electric field will be O O E 300 sin 2 100x 3x 10 0t V m O E 30 sin 27 100x 3 10 t V m Ey 30 sin 27 100x 3 10 t V m Ey 300 sin 27 100x 3 10 0t V m

The magnetic intensity associated with an electromagnetic wave propagating in a non magnetic dielectric medium is given by H 6 cos 6x 2x10 t A m The associated electric field E has an amplitude in V m A 80T B 160T 480T

Two simple harmonic motions with the same amplitude and same frequency acting in the same direction are impressed on a particle If the resultant amplitude of the particle is equal to the amplitude of individuals S H M s the phase difference between the two simple harmonic motions is 2 A 3 C K 4 T B D F N 2 2f 3

For a plane electromagnetic wave propagating in 7 the Z direction which one of the following combination gives the correct possible direction for E and B field respectively 2 X 1 2j and 2 i 21 3i and 31 21 2k 21 35 and i 25 4 3 4 31 4 and 4i 3i you K

Block A and B have masses 40 kg and 60 kg respectively They are placed on a smooth surface and the spring connected between them is stretched by 1 5 cm If they are released from rest determine the speeds of the blocks at the instant the spring became unstretched A V 3 m s V 4 5 m s B V 4 5 m s V 3 m s C V 5 m s V 6 m s D V 4 m s V 3 m s 2

A particle executes SHM with amplitude 0 4 m and time period 24 s The distance travelled by the particle in 10 s is initially particle is at its mean position 1 0 2 m 3 0 8 m 2 0 4 m 4 0 6 m

Jun 15 C An aperiment is carried out to find the acceleration of free fall A strp of paper is attached to a heary object The object is dropped and talks to the ground pulling the paper through a timar The timer marks dots on the paper strip at intervals of 0 020s section of the paper strip with the first three dots marked The fint dot on the Fptshowe paper step labelled A ta marked at the instant the object is dropped 0 0076m 0 0019m paper strip

A uniform cylinder of length and radius r is connected between ice at 0 C and steam at 100 C This leads to melting of ice at the rate of a kg sec Now the cylinder is melted and recast into 3 identical cylinders of radius 2r each and they are now connected in series across the same ice and steam chambers The new rate of melting of ice in kg sec is 1 2a 3 4a 9 2 a 4 6a

Two thermometers one containing mercury and another spirit read same temperature The mercur thermometer has a lower emissivity than spirit thermometer Both have the same area and heat capacity If both are brought in bright sun A The temperature rises at equal rate in both B The temperature rises at higher rate in spirit thermometer C Final steady state temperature will be the same in both tamperatura will ha higher in cpirit thormo D Finol etood atar

2 1 W m 2 9 W m2 9 Assume a bulb of efficiency 2 5 as a point source The peak values of electric and magnetic field produced by the radiation coming from a 100 W d bulb at a distance of 3 m is respectively a 2 5 V m 3 6 10 T b 4 2 V m 2 8 10 T c 4 08 V m 1 36 x 10 T 3 6Vm 4 2 x 10 T d

free space a ko b c d tesla at a 37 The frequency of electromagnetic wave which is best 2 10 k suitable to observe a particle of radius 3 x 10 cm is of the order of a 10 5 Hz c 10 Hz d 3 6 mcy 25 MHz b d 10 4 Hz 10 2 Hz

Hz 38 The electric field part of an electromagnetic wave in vacuum is E 3 1 cos 1 8ady 5 4 10 rad ri m The wavelength of this part of electromagnetic wave is a 1 5 m b 2 m c 2 5 m d 3 5 m

The electric field of a plane electromagnetic wave varies with time of amplitude 2 Vm propagating along z axis The average energy density of the magnetic field in J m is a 13 29 x 10 12 c 17 72 x 10 12 b d 8 86 x 10 12 4 43 x 10 12 el a b c d 55 Th

d both a and b 0 A charged particle oscillates about its mean equilibrium position with a frequency of 10 Ha The frequency of electromagnetic waves produced by the oscillator is a 10 Hz c 10 Hz b 10 Hz d 10 Hz sp b c

A plane electromagnetic wave of frequency 25 MHz travels in free space along x direction At a particular point in space and time electric field E 6 3 V m The magnitude of magnetic field B at this point is a 1 2 x 10 6 T c 2 1 x 10 T 1 2 x 10 T 2 1 10 T b d

3 the electric field in a plane electromagnetic wave is along the y axis and its component is given by Emin lox wt agnetic field is along the z axis and its component is given by 1290 SI units

The electromagnetic waves were produced experimentally by Hertz in 1888 using hertz oscillator which were of wavelength 6m Jagdish Chander Bose in 1895 graduated these waves which were of wavelength 5mm to 25mm and in 1896 G Margoni established a wireless communication between two stations 50 km apart using electromagnetic wave the amplitude of electric field is 10V m The frequency of wave is 5x10 4 Hz The wave is propagating along Z axis 1 If Mo ands are the absolute permeability relative permeability absolute permittivity and relative permittivity of the medium then the velocity of electromagnetic wave in a medium is 1 1 b E a c Hoo 1 HEHE d ME Hoo 2 In electromagnetic wave the average energy density due to magnetic field is a 8 85x10 10Jm 3 b 4 42x10 0Jm 3 c 2 21x10 10Jm 3 d 6 63x10 10Jm 3 3 In electromagnetic wave the total average energy density is a 8 85x10 10Jm 3 b 4 42x10 10Jm

14 Suppose that the electric field part of an electromagnetic wave in vacuum is 3 1 N C cos 1 8 rad m y 5 4 x 106 rad s t i a What is the direction of propagation b What is the wavelength c What is the frequency v d What is the amplitude of the magnetic field part of the wave e Write an expression for the magnetic field part of the wave