Electromagnetic waves Questions and Answers

The electric field in a plane electromagnetic wave is given by Ey 6 2sin 2 4 x 10 1t 8 x 10 x V m then x is in m and t is in s The velocity of electromagnetic wave is 2 4 x 108 m s The wavelength of electromagnetic wave is 1 3 cm The frequency of electromagnetic wave is 3 8 x 10 0 Hz The wave is propagation along z axis

Electromagnetic waves can be produced by Stationary charges Charges in uniform motion min sec Accelerated charged particles Both by stationary charges and moving charges

Electric and magnetic fields are produced by radiations coming from a 12 W bulb The efficiency of the bulb is 80 What is intensity of radiations provided by electric field at 4 m from the bulb assuming it as a point source 0 048 W m 0 03 W m O 0 024 W m O 0 013 W m

Electromagnetic Waves The electric field amplitude in an electromagnetic wave radiated by a 200W bulb at a distance 2m is assuming efficiency of bulb is 10 in converting electrical energy into light energy and bulb is a point source 9 1 LIN V m V m 1 1 8x10 Cs 1 3 4 1x10 Cs 1 10 A parallel plate capacitor is charged to 60 C The plate losses charge at the rate 1 8x10 8 Cs The magnitude of displacement current is 1 11 sin t 3 sin xx10 t 1 2 3 6x10 Cs 1 4 5 7x10 2 Cs 1 11 A plane electromagnetic wave propagating in the x direction has wavelength of 6 0 mm The electric field is in the y direction and its maximum magnitude of 33 Vm The equation for the electric field as a function of x and t may be represented as t is in sec x is in m c is speed of light 2 33 sin 3 33 sin 4 11 sin 1 sin xx10 t 1 1 3 A 3 2 A 2 10 3 V m t 30 7 V m 12 A capacitor is connected across a battery for charging Current through the battery at an instant is 3 A Displacement current through the capacitor at that instant is 2 1 5 A 4 2 5 A 13 An em wave transports energy along y axis If at any instant magnetic field vector is along x axis the electric field vector at this instant is along 1 z axis 3 x axis 2 z axis 4 x axis 14 The electric field in an electromagnetic wave is given by E 100 cos 2 x 106 t 5x Vm 1 The average energy density of E M wave is in S I unit 105 36m 10 3 5 3 36 15 A parallel plate capacitor consists of two circular plates of radius 10 cm If the conduction current is 2 ampere then the magnetic field at 8 cm from the axis of plates due to displacement current is 2E Atc Telegram neetquestionnaper 1 10x10 6 T 2 5x10 6 T 3 15x10 T 4 25 10 T 16 A plane electromagnetic wave is incident on a plane surface of area A perpendicularly If the surface absorbs the radiation falling on it completely and if E is the energy that strikes the surface in time t then the average radiation pressure exerted on the surface is where c speed of light E Atc 10km 00 Aakash Institute 105 72 2 10 5 72n 4 Im Et Ac 17 In a wave E 100 v m Find the magnitude of poynting s vector 1 13 25 W m 2 26 5 W m 3 18 25 W m 4 19 7 W m2 18 The average energy density of an electromagnetic wave given by E 50N C sin at kx will be nearly 1 1 1x10 8 J m 2 10 7 J m3 3 10 6 J m 4 10 5 J m3 19 The intensity of a plane electromagnetic wave is 5 W m It is incident on a perfectly reflecting surface Find the radiation pressure 1 3 33 x 10 9 N m 3 8 0 10 8 N m 2 3 33 x 10 8 N m 4 8 0 x 10 9 N m

For an electromagnetic wave described by B 8 x 10 6 sin 5000x 3 x 1011 nt where B is in tesla x is in metre and t is in second the incorrect parameter is 1 Frequency 1 5 x 10 1 Hz 2 Wavelength 4 0 10 4 m 3 Speed 6 0 x 107 ms 1 4 4 Maximum electric field is 320 Vm 1

EXAMPLE 10 10 Given a uniform plane wave in air as E 40 cos ot Bz a 30 sin oot Bz a V m a Find H b If the wave encounters a perfectly conducting plate normal to the z axis at z 0 find t reflected wave E and H c What are the total E and H fields for z 0 d Calculate the time average Poynting vectors for z 0 and z 20

Two ends of an inductor of inductance L are connected to two parallel smooth horizontal conducting rails A conducting rod of length and mass mis given velocity vo as shown The whole system is placed in uniform magnetic field B directed vertically downward then 1 Decca pc dec Az 44 d2 fag kul u a fu ga 1 A A A ka ggsy gwmu a B Ga llllllll L v vo v vo HI H YH JAG G3 h Tr la 1 atyof Aciu ch fur V V0 COS Vo 1 sin t A Speed of the rod as a function of time vo 1 sin t Bl D m 22 L F Correct Answer Bl mL B x4 93 ud B Speed of the rod as a function of time V V0 COS t mL agu H had 64 93 h u te 2 Correct Answer X X C Time taken by the rod to come to rest for T mL first time is 2Bl GTR z faghaz 307 am agu T mL 2Bl Maximum current in inductor is

29 If H 2 cos et kz i in an EMW propagating along z axis then electric field is given by 1 753 cos ot kz j 2 387 sin ot kz j 3 753 cos wt kz 4 753 sin cot kz j

Given light as described by El Ege x w where E is the magnitude of the electric field O The direction of light propagation is along x O The electric field points along x O The direction of light propagation is along x and the electric field points along x none are correct

the suns frequency is 510 THz Jayson takes a trip that is 7 856 light years away from earth in earths frame During his trip he observes the suns frequency to be 204 THz A determine time his trip takes from perspective of someone on earth B determine time his trip takes from his perspective

The electron in the hydrogen atom revolves around th 0 nucleus in an orbit of radius 0 5 A What is the equivalent magnetic moment if the frequency of revolution of the electron is 101 MHz A 0 8 x 10 23 Am B 1 1 x 10 2 22 Am C 1 256 10 23 Am

40 MHz travels in free space in the X direction At some point and at some instant the electric field 106 has its maximum value of 750 N C in 10 Y direction The wavelength of the wave is 1 3 5 m 2 5 5 m 3 7 5 m 4 9 5 m EM0228 3 4 5 6 In Q 2 the period of the wave will be 1 2 5 us 2 0 25 us 3 0 025 us 4 none of these EM0229 In Q 2 the magnitude and direction of magnetic field will be 1 2 5 T in X direction 2 2 5 T in Y direction 3 2 5 T in Z direction 4 none of these EM0230 In Q 2 the angular frequency of e m wave will be in rad s 1 8 TX107 3 2 TX105 2 4 x106 4 x104 EM0231 In Q 2 the propagation constant of the wave will be 1 8 38 m 3 4 19 m 2 0 838 m 4 0 419 m

20 W Incident on a surface 60 light is absorbe rest reflected find magnitude of average force on the surface A 8 104 N B 9 3 x 108 N C 9 3 108 N D 1015 N

The sun delivers 103 W m of electromagnetic flux to the earth s surface The total power that is incident on a roof of dimensions 8m x20m will be 1 6 4 x103 W 2 3 4 x 104 W 3 1 6 105W 4 none of these EM0233 In Q 7 the radiation force on the roof will be 1 3 33 x 10 5 N 3 7 33 x 10 N 2 5 33 x 104 N 4 9 33 x 10 N

Two point charges q and q2 are of magr 2 C and 2 C respectively are place m apart as shown in figure The ratio of e field at a point A to the point B will be B 1 0 2 m 32 3 2 C 0 1 m A 2 4 3

A uniformly charged semi infinite wire having inear charge density 2 x 10 10 C m is placed along x axis as shown Find electric lux in SI units through a ring of radius r 10 m centred at origin and lying in v z plane

1 Given the following waves draw the superposition of the waves as the left side of the triangle is at the left point of the square points A and B meet B A

A square loop of side 15 cm carrying a steady current of 5 A is placed with its one side parallel to a long straight conductor carrying a current of 10 A as shown in figure The correct statement related to net force experienced by the loop due to wire is A B C D 5 cm 10 A SA C repulsive in nature having magnitude equal to 3 75 x 10 5 N repulsive in nature having magnitude equal to 2 25 x 10 5 N attractive in nature having magnitude equal to 2 25 x 10 5 N attractive in nature having magnitude equal to 3 75 10 5 N

HOW TO GET DIRECTION OF PROPAGATION OFWAVE FRO M SUCH EQUATONS PLEASE EXPLAIN how to get direction of E M Oscillating magnetic field in a plane electromagnetic wave is given by 6 4 x 10 6sin 9 x 10 t 30x tesla Expression for oscillating electric field in N C will be E 600 sin 9x10 t 30x k 600 sin 9 10 t 30x k E 1200 sin 9x10 t 30x k E 1200 sin 9x10 t 30x k

An electromagnetic wave travelling in a vacuum is given by E 1 E jE cos kz wot The associated magnetic field of the wave is given by A B 1E E cos kz wt C 1 B B E E cos kz wt C 1 C B E E cos kz wt C D B E E cos kz wt C

Two parallel disks 60 cm in diameter are separated by a distance of 15 cm and completely surrounded by a large enclosure at 100 C The properties of the surfaces are T 540 C 0 7 T 300 C 0 5 What is the net radiant heat transfer with each surface Do not include back side exchange only that from the surfaces facing each other

If denote microwaves X rays infrared gamma rays ultra violet radio waves and visible parts of the electromagnetic spectrum by M X I G U R and V the following is the arrangement in ascending order of wavelength A B C R M I V U X and G M R V X U G and I G X U V I M and R 1 M R U V X and G Stry X

A lamp emits monochromatic green light uniformly in all directions The lamp is 3 efficiency in converting electrical power to electromagnetic waves and consumes 100 W of power The amplitude of the electric field associated with the electromagnetic radiation at a distance of 5 m from the lamp will be nearly A B skipped C D 1 34 V m 2 68 V m 4 02 V m 5 36 V m Stry N

The laser beam from a source which radiates energy at the rate of 25 W and wavelength 5000 A is focus on a perfect absorbing surface having area equal to square of wavelength of beam The radiation pressure on surface is Only one correct answer A B C 0 33 N m 1 44 N m 1 33 N m

The temperature dependence of the electrical conductivity or of two intrinsic semiconductors A and B is shown in the figure If EA and EB are the band gaps of A and B respectively which one of the following is TRUE a EA EB c E ER In o B T b EA EB d E and Eg both depend on temperature

ommon Data for Q 81 and Q 82 Let E E exp ik F wot where k 2 k cos ik sin o k 1 and 2 and 2 are cartesian unit vectors represent an electric field of plane electro magnetic wave of frequency Which one of the following statements is TRUE a The magnitude of the electric field is attenuated as the wave propagates b The energy of the e m wave flows along the x direction c The magnitude of the electric field of the wave is a constant d The speed of the wave is the same as c speed of light in free space The magnetic field B of the wave is a y Eo exp zk sin o exp i zk cos ot b y Eo exp zk sin exp i zk cos cot c Eo exp i zk cos cot 4

AC ant na da he P Q vii A circuit with R 700 in series with a parallel combination of L 1 5H and C 30uF is driven by a 230V supply of angular frequency 300 rad s a Find the impedance of the circuit b What is the RMS value of total current c the circuit d zerol What are the current amplitudes in the L and C arms of How will the circuit behave at 1 LC a 163 32 b 1 414A c 0 653A 2 64A d Circuit current becomes

along x axis is given as Ey 30 sin 4 10 x 1 5 x 10 1 V m The frequency propagating wave is NCERT Pg 2 1 5 GHz 2 17 6 GHz 3 23 9 GHz 4 15 4 GHz

If y a sin bt cx where y and x represent length t represents time then which of the following has the same dimensions as that of ab ab X Speed 2 2 Momentum 3 Angle 4 Acceleration bf c 0 26d 1 26 216 610 214 C

xii In the circuit shown in figure 5 123 switch S is closed at time t 0 Find the current through the inductor as a function of time t i 5 1 e 20001 3 A 2V H 4V www 252 ww 192 vooooo L 1mH Figure 5 123

Q2 For a plane electromagnetic wave the amplitudes of electric Eo and magnetic fields Bo are related to each other as O A Bo Eo C where c is the velocity of light in vacuum O B Eo Bo c where c is the velocity of light in vacuum O c Bo Eo c where c is the velocity of light in vacuum O D Eo Bo C where c is the velocity of light in vacuum

If escape velocity on the surface of a planet is Ve If planet shrinks such that its radius decreases to 1 4 of present radius without mass changing The escape velocity on its surface is 1 2Ve 2 Ve 3 Ve 2 4 Ve 4

Electromagnetic radiations of intensity 1 W m2 strikes on the surface of a substance which reflect 80 incident radiation back into same medium The radiation pressure on the surface of substance is Only one correct answer A 4 10 8 N m B 2 5 x 10 7 N m C 8 x 10 8 N m D 6 x 10 9 N m i

A plane electromagnetic wave propagating in the x direction has a wavelength of 60 mm The electric field is in the y direction and its maximum magnitude is 33 Vm The equation for the electric field as function of x and tis A 11sint t x c B 33sin x 10 0 t x c C 33sin t x c D 11sina x 10 t x c A A B B C C

Consider a series LCR circuit C R L foroors XL 3002 R 2002 Xc 100 The equation for ac voltage source is given as V t 100 2 sin wt Choose the correct statement s The equation for voltage across inductor as V t 150 sin wt The equation for voltage across inductor as V t 50 sin wt The impedance of LCR circuit is 20 2 ohm O The equation of voltage across capacitor is Vc t 50 sin wt 37

In a plane electromagnetic wave electric field varies with time having an amplitude 1 V m1 The frequency of wave is 0 5 x 1015 Hz The wave is propagating along x axis The average energy density of electric field is O 1 1 10 12 J m 3 2 2 x 10 12 Jm 3 3 x 10 2 Jm 4 4 x 10 12 Jm

R have tric spherical shells of radius R 9 92 charge respectively as shown in figure How much charge will flow through key k when it is closed 1 92 3 92 R R R R 0 R R R k 9 3 4 92 w 2 q R 9 R R Ri R 3 pow 9 R R 0 R RIK Q XV 6 7

What is the velocity of a beam of electrons that goes undefiected when moving perpendicular to an electric and magnetic fields E and B are also perpendicular to each other and have magnitudes 6500 V m and 4 1x10 3 T respectively Express your answer to two significant figures and include the appropriate units V 1 6x108 Previous Answers Correct Correct answer is shown Your answer 1 59 100 was either rounded differently or used a different 111

9 A red LED emits light at 0 1 watt uniformly around it The amplitude of the electric field of the light at a distance of 1 m from the diode is a 1 73 V m c 5 48 V m b 2 45 V m d 7 75 V m JEE Main 15

4 For plane electromagnetic waves propagating in the z direction which one of the following combinations gives the correct possible direction for E and B fields respectively a 2 3 and 2 b 2 3 and 3 2 c 3 4 and 4 3

Which of the following statements is incorrect about LED 1 It require low operational voltage 2 It has fast on off switching capability 3 The band width of emitted light is 100 A to 10000 A 4 It does not require warm up time

3 In a plane electromagnetic wave the electric field oscillates sinusoidly at a frequency of 2 x 100 Hz and amplitude of 48 V m The frequency of oscillation of magnetic field will be 1 2 x 10 Hz 2 16 10 0 Hz 3 2 10 0 Hz 4 16 x 100 Hz

If at x 2m and t 2s the particle is at y 1mm and its velocity is in positive y direction then th equation of this travelling wave is y is in mm t is in seconds and x is in metres 100 nt 30 A y 2 sin C y 2 sin TTX 2 TX 2 100 rt 150 TX B y 2 sin 100 nt 120 2 D None of these

Monochromatic A at an angle light of intensity I falls over a blackened plate of area as shown in the figure If 70 of light is absorbed and mass of plate is m Find the acceleration of plate given wave length light is 2 Take 0 60 and no other force except radiation acting on the plate

4 If 0 and Ho are the electric magnetic permeability in free space and are corresponding quantities in a medium then index of refraction of the medium is a EHO EHO b d E 0

Magnetism is relativistic Reason When we move along with the charge so that there is no motion relative to us we find no magnetic field associated with the charge ONO Statement 1 is Ture statement 2 is True Statement 2 is a correct explanation for statement 1 Statement 1 is True statement 2 is True statement 2 is NOT a correct explanation for statement 1 Statement 1 is True statement 2 is false Statement 1 is false statement 2 is True

where c is the velocity of the light Equating both the equations we get h mc h h mc P or iii de Broglie suggested that the above equation is applicable to any material particle The mass of a photon is substituted by the mass of material particle and the velocity cis substituted by the velocity v of the material particle say electron Thus for an electron we can write h mu h P 2 gnituite du

A transverse wave travels on a taut steel wire with a velocity of v when tension in it is 2 06 x 10 N When the tension is changed to T the velocity changed to v 2 The value of T is close to 1 10 2 x 102 N 3 2 50 x 10 N 2 5 15 x 10 N 4 30 5 x 104 N

A plane electromagnetic wave of frequency 25 GHz is propagating in vacuum along the z direction At a particular point in space and time the magnetic field is given by B 5x10 JT The corresponding electric field E is speed of light c 3 x 10 ms 1 1 1 66 x 10 16 V m 2 15 i V m 3 1 66x10 V m

A modulating signal is a square wave as shown in figure 1 m t in volts FIGURE 15 14 2 t in seconds The carrier wave is given by c t 2 sin 8t volts i Sketch the amplitude modulated waveform ii What is the modulation index