Magnetism and Electromagnetic Induction for JEE (Advanced), 3rd edition 9353503728, 9789353503727

Citation preview

Contents

1.29 Moving Coil Galvanometer

1.30

vii

Preface 1.

Construction

and Magnetic Magnetic Field

1.1-1.64

Forces

Introduction

in a Magnetic Field Force on a Moving Charge Units of Magnetic Field Strength

Theory of the Current Sensitivity

Galvanometer

1.30

1.1

of the Voltage Sensitivity

Galvanometer

1.30

1.1

1.2

Conditions

for Determining the Direction Right Hand Rules of the Magnetic Force Acting

on a

1.2

1.1

Concept Application Exercise Field Motion of a Charged Particle in a Magnetic Field Charged Particle Entering into Magnetic Region from Outside

If Particle is

Projected at Some Angle with

Magnetic Field (Helical Paths) Path of a Charged Particle in Both Electric and Magnetic Fields

Applications Involving Charged

Particles

Galvanonmeter

Exercise

1.4

Single Correct

1.5

Answer

Type

1.5

Type Multiple Correct Linked Comprehension Type

1.6

Matrix Match Type Numerical Value Type

Answers

Archives Answers Key

1.9 1.11

Moving

2.

Magnetic Field Due to Current Element:

Velocity Selector

1.12

Biot and Savart Law

Magnetic Field

1.49 1.52 1.57 1.58 60

2.1

Introduction

2.1

1.12

Direction of Magnetic Field Due to a Straight

1.14

Current Carrying Wire a

1.15

Field Due to Carrying Wire Field Due to

a

Magnetic

Motion of a Charged Particle in Non-Uniform

1.41

2.1-2.61

Sources of Magnetic Field

1.12

Cyclotron

1.31

1.63

in a Magnetic Field

Mass Spectrometer

1.30

1.32 1.41

Exercises

1.3

Lorentz Force

for Sensitive

Concept Application Solved Examples

Moving

Charged Particle

1.30

2.2 Straight Current

2.3

Straight Current

Concept Application Exercise 1.2

1.16

Magnetic

Force on a Current-Carrying Wire

1.17

Carrying Wire of Intinite Length

1.17

Straight Wire

2.4

1.18

Magnetic Induction Due to a Large Current Carrying Sheet

2.8

Magnetic Field Due to a Semi-lnfinite

Magnetic Force Acting on a Current Carrying

Conductor Direction of Force on a Current-Carrying Wire in Magnetic Field Concept Application Exercise 1.3

1.23

Magnetic Dipole and Dipole Moment

1.24

Torque on a Current-Carrying Planar Loop in a

2.3

Concept Application Exercise 2.1 Magnetic Field at the Center of a Cireular Coil Concept Application Exercise 2.2

2.9 2.10 2.14

1.26

Magnetic Field of a Circular Current Loop

2.15

Energy of Dipole

1.28

Finding Magnetic Field Inside a Long Solenoid

2.16

Work Done in Rotating a Current-Carrying Coil in Magnetic Field

1.29

Uniform Magnetic Field

Force Between Two Infinite Parallel

Current-Carrying Wires

2.18

Concept Application Exercise 2.3

2.20

iv Contents

Exercise 3.2

2.21

Ampere's Law

Ampere's Law Guidelines for Applying Wire Induction Due to a Cylindrical

Magnetic

Magnetic

Hollow Induction Due to a

Due to

a

Large and Thick

Current Carrying Sheet

Magnetic

Intensity of Magnetization

2.25

2.28 2.39 2.39

Single Correct Answer Type Multiple Correct Answers Type

2.49

Linked Comprehension Tipe

2.51

Matrix Match Type Numerical alue Type

2.54 2.56 2.57

Archives Answers Key

2.60

3. Permanent Magnets and Magnetic 3.1-3.32

Properties of Matter Introduction

3.1

Bar Magnet

3.1

Properties of Bar Magnet

3.1

Strength of Bar Magnet

3.2

Magnetic Field Magnetic Field Lines Coulomb's Law of Force Between Two Magnetic Poles A Small Current-Carrying Coil as a as a

Magnetic Dipole Bar

Magnet

Magnet Magnetic Field at Any Point Due to a Short

Magnetic Dipole Torque on a Bar Magnet in a Magnetic Field Potential Energy of a Bar Magnet Placed in a Magnetic Field

Concept Application Exercise 3.1 Earth's Magnetism

Magnetic Elements of the Earth of a Bar

Find

Tangent Law

3.17

Magnetic Permeability (4)

3.17

Magnetic Flux

3.17 3.17

4.

Paramagnetic Substances

3.17 3.18

Ferromagnetic Substances

3.18

Paramagnetism on Basis of Electron Theory

3.19

Ferromagnetism Hysteresis

3.19 3.20

Salient Features of Hysteresis Loop

3.20

Soft and Hard Magnetic Materials

3.20

Concept Application Exercise 3.3

3.22

Solved Examples

3.22

Exercises

3.27

Single Correct Answer Type Archives Answers Key

3.27 3.32 3.32

Electromagnetic Induction

4.14.66

3.2

4.1

Magnetic Flux

4.1

3.2

3.3

Magnetic Field on Equatorial Line of a Bar

to

Magnetic Susceptibility (Xm)

Introduction

3.3

Neutral Point and

3.16

3.2

Magnetic

Magnetic Field on Axial Line of a

3.16

Diamagnetic Substances

2.2

Exercises

Atom

3.16

Classification of Magnetic Materials

Exercise 2.4

Dipole

3.16

Total Magnetic Field or Induction

2.27

Toroid Magnetic Field of a

3.15

Magnetic Intensity

2.26

Field of a Solenoid

Concept Application Solved Examples

2.23

2.24

Cylindrical Wire

Magnetic Induction

2.22

Concept Application Materials Magnetic Properties of

3.4

3.5

Flux Linkage Work Done i

4.2

Changing Orientation of a Current

Carrying Coil in Magnetic Field Faraday's Law of Electromagnetic Induction Direction of Induced EMF Induced Charge Lenz's Law

Concept Application Exercise 4.1 3.6 3.7

Motional Electromotive Force

Finding Direction of Induced EMF Special Cases

3.7 3.9

3.9 3.10

Magnetic Moment 3.11

Tangent Galvanometer

3.12

Deflection Magnetometer Vibration Magnetometer

3.13 3.13 3.14

Motional EMF

4.4 4.5 4.6

4.8 4.8

4.13 4.14

4.15 4.15

as an

Motional EMF

in a in Magnetic Field

Equivalent Battery

Random

Shaped Wire Moving

Concept Application Exercise 4.2 EMF Across Rotating Straight Conductor Motional EMF when the Magnetic Field is Non-Uniform Concept Application Exercise 4.3

Induced Electric Field Induced EMF in a

4.16

Stationary Conductor

4.16

4.22 4.23 4.26

4.26 4.27 4.27

Contents V 4.28

Time-Varying Magnetic Field

4.29

Forces Electric Field Lines of

Concept Application Sohved Examples

4.32

Exercise 4.4

4.33

4.40

Exercises

4.40

Single Correct Answer 7ype Multiple Correct Answers Tpe Linked Comprehension Tipe

4.51 4.54 1.59

Matrix Match Tipe Numerical Value Type

4.62 4.64

Archives Answers Kev

4.66 5.1-5.47

5.

Inductance

or

AC Circuits

Only Inductor Only Circuits Containing

Resistor AC Circuits Containing

AC

5.1 5.1

Self-Inductance

5.1

EMF Direction of the Self-Induced

5.2

Inductance of a Solenoid

5.3

Mutual Inductance to

a

5.5

Pair of Coils

Two Calculation of Mutual Inductance Between

Capacitor AC Circuits Containing

Only

Resistor, Inductor, and AC Circuit Containing in Series (Series LCR Circuit)

Capacitor

LCR Circuits Power in Series of Current

Wattless Component

in Series LCR Circuit of Resonance 0-Factor (or Quality Factor)

Another Definition of Q-Factor

Skin Effect

Concept Application

Exercise

6.1

Solved Examples

Linked Comprehension Type

Series Combination

5.6

Parallel Combination

5.7

Matrix Match Type Numerical Valhue Type

5.8

Analogy Between Self-Induction Concept Application Exercise 5.2

and Inertia

5.10 5.10

Concept Application Exercise 5.4

6.10 6.10

7. Electromagnetic Waves

6.13 6.13

6.19 19

6.23

6.24 6.26 6.27 6.27

6.29 7.1-7.9

Maxwell's Equations

1.2

Electromagnetic Wave Spectrum

Energy Density

7.3 7.3

5.19

Intensity

1.3

5.22

Momentum

1.3

Properties of Electromagnetic Waves

7.3

Atmosphere Troposphere

7.4

Stratosphere

7.4

Mesosphere lonosphere

7.4

Solved Examples

7.5 7.7

5.15 5.17

5.18

Solved Examples

5.22

Exercises Single Correct Answer Type

S.29

29

Multiple Correct Answers Type Linked Comprehension Type

5.3 .38

Matrix Match Type

5.43

Numerical Value Type Archives

5.44

Answers Key

5.47

6. Alternating Current

6.9

Maxwell's Displacement Current

5.12

Oscillation of Electrical and Magnetic Energy

6.9

7.1

Decay of Current

Oscillations in an LC Circuit

6.5 6.8

7.1

5.11

Inductor

6.4

Introduction

Growth of Current

Concept Application Exercise 5.3 Energy Stored in the Magnetic Field of an

Archives Answers Key

5.11

Growth and Decay of Current

6.4

6.12

Combination of Inductors

Inductor in Electrical Circuits

6.4

6.11 Transformers

5.6

5.1 Concept Application Exercise

6.3 6.3

6.9

Choke Coil

5.6

Coils from Their Self-Inductance

6.2 6.3

Capacitive Reactance

Exercises Single Correct Answer Type Multiple Correct Answers Type

5.5

6.1

Inductive Reactance

Resonance

Introduction

Total Flux Linked

Current Average Value of Value of Current Root Mean Square (RMS)

Mean

5.45

6.1-6.29

Introduction

6.1

Phasor Diagrams

6.1

Exercises Single Correct Answer Type

1.4

7.4

7.7

Archives

7.9

Answers Key

7.9

vi

Contents

Solutions

S.1-S.114

Chapter 1

S.1

Chapter 2

S.27

Chapter 3

S.50

Chapter 4

S.58

Chapter 5 Chapter 6 Chapter 7

S.84S.103 S.I13

Appendix:

Chapterwise Solved January 2019 JEE Main Questions (All Sets)

A.1-A

7

Electromagnetic Waves

NTRODUCTION in 1865, Maxwell discovered ght together the

the

phenomenon

displacement

of

electricity

current. This

and

magnetism Coherent and unified theory. After this discovery, Maxwell

MAXWELL'S DISPLACEMENT CURRENT According to Ampere's circuital law, the magnetic field B is related to steady current I as

dicted the transmission of energy by electromagnetic waves,

B dl

shich could travel with the speed of light. This led him to mnclude that the light itself is an electromagnetic wave. According to

him,

an

accelerated

sinusoidal time-vary1ng magnetic field,

charge

which in

produces turn

a

produces

asinusoidal time-vary1ng electric field. The two fields so

roduced are mutually perpendicular time-varying electric and magnetic fields. They constitute electromagnetic waves which an propagate through empty space. The velocity of electromagnetic waves in free space is given

..(i)

where I is the current path C.

travelling

the surface bounded

by closed

In 1864, Maxwell showed that relation (i) is logically inconsistent. He accounted for this inconsistency as follows:

Consider

a

parallel plate capacitor

having plates P and Q being charged with battery B. During charging, a current I flows through the connecting wires which changes with time. This current will

c=

produce magnetic field around the can be detected using a magnetic compass needle. Consider two loops c, and c, parallel to the plates P and Q of the

wires which

wdere 4 =1.257x 10-6TmA-) and E, (=8.854 x10-12 CNm2) TE, Tespectively, the absolute permeability and the absolute pemittivity of free space. The velocity of electromagnetic waves

u ree

space

(vacuum)

is

1e,3 x 10 m s.

equal to

the

velocity of light in vacuum,

capacitor. C is enclosing only the connecting wire attached to the plate P of the capacitor and c, lies in the region between the two plates of capacitor. For the loop c,, a curent I is flowing through it, hence Ampere's circuital law for loop c, gives

B

LLUSTRATION 7 1

d

(11)

C

What physical quantity is the same for X-rays of wavelength Um, red light of wavelength 6800 Å, and radiowaves of

wavelength 500 m?

Since the

loop c,

lies in the region between the plates of the curTent flows in this region. Hence Ampere's circuital law for loop c, gives

capacitor,

no

B-di 0

Speed is the physical quantity which is the same in

vacur

um for given X-ray, red light and radiowave.

O f speed of electromagnetic waves in vacuum is

C3x103 m s.

ii)

C The relations (i) and (iii) continue to be true even if two loops c, and c, are infinitesimally close to the plate P of the capacitor. On the other hand, as the loopsc, and c, are infinitesimally close. it is expected that

LLUSTRATION 7.2 Pdne electromagnetic wave travels in vacuum along electric CtIon. What can you say about the directions of its and 30

Mgnetic

field vectors? If the frequency of the

Hz, what is its

re are in

he

the xy

wave is

wavelength

electric field

vector

E

plane.

USing c= v, we get

C

V

and

and

magnetic

3x10 1=

30x60

field vector B

C

(iv)

C

Thus, relation (iv) is in contradiction with relations (ii) and

(il). This led Maxwell to point out that Ampere' s circuital law given by (i) is logically inconsistent.

Idea of Displacement Current: Maxwell predicted that not e conductor produces magnetic fiela Only a current flowing in a also a time-varying electric field (1.e., changing electric in a vacuum/free space (or in a dielectric) produces a

electric field)

=10 m

as

magnetic field.

7.2

Magnetism and Electromagnetic Induction

It means a changing electric field gives rise to a current which flows through a region so long as the electric field is changing there. Maxwell also predicted that this current produces the same

magnetic field

as a conduction current can

produce.

This current

=

The Lorentz equation is

is known as 'displacement current".

F=q(xixB

Thus, displacement current is that current which comes into play in the region in which the electric field and hence the electric

E, = Ez) sin (of-ky)

flux is changing with time.

B,

Maxwell defined this displacement current in space where electric field is changing with time as (V)

where o is the electric flux. Maxwell

also

found

that

conduction

current

()

and

displacement current (,) together have the property ofcontinuity

d+4

4hequation: d i 4

-ky), where

Bxy sin (

=

and k Since = 2f, where fis the frequency the wavelength.

=

2tn, where 1is

Therefore, 2T= 27/ fa But f gives the velocity of the

wave.

Hence fA

=

c

=

k.

Hence,

the velocity of the waves is given by 1

although, individually, they may not be continuous. This idea led Maxwell to modify Ampere's circuital law in

C

order to make the same logically consistent. He states Ampere

LLuSTRATIDN 7.4

circuital law to the form,

Suppose that the electric field amplitude of an electromagnetic

B-dl =(0+1p) =%I+ ddt

wave is E

Determine

(a)

It is now called as Ampere Maxwell law.

1 2 0 N/C and that its frequency is v = 50.0 MHz

B.

,

k,

and A.

(b)

Find

expressions

for E

and B.

ILLUSTRATION 7.3

Sol

The following figure shows capacitor made of two circular

plates.

The

capacitor

is

being charged by

an

external

(a)

(i)

E.n

Using-

Bmax

source

which supply constant current equal to 0.15 A. Obtain

displacement charged by

a

constant curent across

plates.

= C, we get

Dmax

Given

=187x10 Vs

E

120

C

3x103

= 40x10T

1.e., Bay = 400 nTT max

dt

ii) =2av= 2x Tx 50 x 10 3.14x 108 rad s

Sol Displacement current 4 But

= EA = A

=

=

iv)

9_% dadq, E di

Here I= 0.15 A

(ii) k = -272x3.14 =1.05 rad s

doc

=

(b)

E

3x10

= S0x 105

n

=Emax Sin(kr - or)j

120sin(1.05x -3.14 x 10* x)j

dt

I=0.15 A

c = Av or A =

B

Bmax sin(kx - ør)k =

400

sin(1.05r-3.14 x

10 x r)k

MAXWELL'S EQUATIONS

TLLUSTRATION 7.5

The four Maxwell's equations and Lorentz force law together constitute the foundations of classical electromagnetism. The

Suppose that the electric field part of a electromagnetic wav

Maxwell's equations are:

in vacuum is

E (3.1 NC) cos (1.8 rad/m)y + (5.4x 10 rad/s) =

1"equation:

-

4S

=

'equation: ã - dÑ = 0

3dequation:

(a) What is the direction of propagation? (b) What is the wavelength A? (c) What is the frequency v? (d) What is the amplitude of the magnetic field part wave?

of me

write an expression for the magnetic field part ofthe wavc

Electromagnetic Waves

3. lcos {1.8y + (5.4 x Here E 50 with standard equation mparing it cos(kr + wr)d =

7.3

10°)r}i

Comp

E =Ep

(a)

density

is

equal

to the

magnetic density

in average,

27 =3.5 m

Using &=weget A= 5.4x10°

v =-: ic) Frequency, )

Thus, the electric energy

d i r e c t i o n

OT,

= 0.86 MHz

27T

4 Ho

c = o r B-E=_31

C

3x1o810nT

B

e) B=

10

INTENSITTY cos(1.8y +5.4 x 10$)

The energy

crossing

per unit

area

per unit time

perpendicular to

the direction of propagation is called the intensity of a wave.

FLECTROMAGNETICWAVE SPECTRUMM

CAt

Rrudly. the various regions of the electromagnetic wave gctrum may be assigned the wavelength ranges as follows:

10-2 10

10-15

106

10-3

100 103

in

10 -

-

meres y-Rays

UVIR

----

Consider a cylindrical volume with area of cross section A and length c Ar along the x-axis. The energy contained in this cylinder crosses the area A in time At as the wave propagates at speed c. The energy contained is

Radio waves

Heat radiations

X-Rays

Power

Microwaves

Wa aves

U=

(c Ar)A

U The intensity is I=AAt

ENERGY DENSITY The electric and magnetic fields in a plane electromagnetic wave

given by E Eg sin ø(t-xlc) ad B= B, sin @(1 xlc)

= UC in terms of maximum electric

ficld,I=eo Ee

=

MOMENTUM

-

The electromagnetic wave also caries linear momentum with it. The linear momentum carried by the portion of wave having

any snall volume dV, the energy of the electric field is

energy Uis given by p = Ulc.

d the energy ofthe magnetic field is Up = B

Thus, if the wave incident on a material surface is completely absorbed, it delivers energy U and momentum p =Ulc to the surface. If the wave is totally retlected, the momentum delivered is 2Ulc because the momentum of the wave changes tromp to -p. It follows that electromagnetie waves incident on a surface

dV

24 Itis, the total energy is U =e, E2 dV 24

Iheenergy density 1s

u

to

24Z

dV

exert a force on the surface.

PROPERTIES OF ELECTROMAGNETIC

B

WAVES (a) In electromagnetie waves the electrie tield vector Ë.

E sin? ot - xlc)+B sin aot- xle)

magnetic field vector B and propagation vector k are

2Ho

wettake the ave verage

Verage value of 1/2

over a

long

mutually perpendicular such that E, B, and k torm a right

time, the sin' terms have

an

angle system. Hence electromagnetie waves are transverse (b)

in nature. Electromagnetice waves travel with speed of light. In vacuum

their speed is

Now,

oCB

and HoE%

=so that,

Ho

and

Eoc

7.4

Magnetism and Electromagnetic Induction

aB

In isotropic medium, their speed is

ox Electromagnctic

(h)

cxert pressure

momentum

carry surfaces, which

waves

(P) on

is

hence

and

known

as

can

radiation

wave with Poynting vector an clectromagnetiC pressurc. For absorbing surface. S, incident upon a perfectly

where n = u , E, is the refractive index of the medium,

P= C

=relative permeability of medium, and relative permittivity of medium or electric dielectric

and if incident upon

E=

direction of (c) The Poynting vector S E x H represents the energy fiow per unit area per second along the direction of

C

=

wave propagation. Its unit is Wm2. The medium offers hindrance to the propagation of wave. value Such a hindrance is called Wave Impedance (Z) and its in a medium is given by

The electric and

)

E

a

sinusoidal plane

the positive x-direction

B B , sin (kx-ot)

and relative

For vacuum or free space

propagating

in

E sin (kx - or)

angular wave given by

permeability

fields of

can also be written as

(.. = 4 , Ho and &: Eg E, ) and e, are relative where , permittivity of the medium.

magnetic

wave

electromagnetic

angular frequency

where @is the

Z=

perfectly reflecting surface, then

25

constant.

(d)

a

=

of the

wave

27f

and k

=

is

intensity ofa sinusoidal plane electromagnetic vector taken over defined as the average value of Polynting wave

The

)

376.6

one cycle.

VEo Also in free space

ATMOSPHERE atmosphere of earth extends upon about below. composition of atmosphere is as given

The

B H

and k is the

number or propagation constant which are

o VE

300 km. The

TROPOSPHERE B

This layer extends up to a height of about 12 km. etc. Density consists of water droplets, vapour, dust particles of air decreases as we move from bottom to top of this layer

Hofo

Troposphere

E= Bc (e) In free space The electrostatic energy density is equal to magnetostatie

energy density. Average electric energy density =Average magnetic

affecting our environment. energy

density

STRATOSPHERE This layer extends from about 10 km to about 50 km. In the uppet or of ozone. The density we have a the

layer atmosphere, part of air at the top of the stratosphere is about 10 times he density d

4o Total average energy density = e E

Cin free space)

(f) In a medium

Magnetic energy density Total energy density

The

=

B 244

B =eE" + 2

The electric and magnetic fields satisfy the following wave equations, which can be obtained from Maxwell's third and fourth equations.

0E

the surface of earth.

MESOSPHERE

Electric energy density =

(g)

This layer is responsible for all the weather phenomena

mesosphere extends from about 50

kn. km to about 80

loNOSPHERE

Th:s

The atmosphere above the mesosphere is called ionospc

rest

layer is composed partly of electrons and positive 1ons: 1 of the atmosphere is composed mostly of neutral molecules The atmosphere is transparent to visible radiation an

We

most

can see the sun and the stars through it clearly. Howevc hy

is absorbed event

able to pass through, it also preve Low lying clouds in the mosphere

infrared radiation is

not

as

the atmosphere. infrared radiation from passing through. The ozone ly the passage of ultraviolet radiation from the sun.

locks

Electromagnetic Waves

LUSTRATION 7, 7.6

the power S ViSibleradiation. Wha

of

sadhation Ata

)

distance distance

is the average

ofl m from

intensity of visible

XAMPLE 7.1

of 10 m?

power

=

of radiation at 1 Average intensity

5

Power

0.4 W

=

5

2

EXAMPLE 7.2

m

According

= 0.004 W m

Sol. (3)

are

electromagnetic cm

famous

some

numbers

em

in physics.

According to the

EM

theory, the vibration magnetic field

Maxwell's EM

electric and

each belongs. spectrum of which emitted

by

atomic

EXAMPLE 7.3

f+elds electric and magnetising wave, the electromagnetic In maximum energy flow is and 0.265 Am. The are 100 Vm an

hydrogen

in

arising from two close b) 1057 MHz (frequency ofradiation as Lamb shift) known energy levels in hydrogen, radiation associated with the isotropic

) 2.7 K (temperature the "big-bang' to be a relic of filling all space-thought origin of the universe) lines of sodium) d) 5890 Å-58963 Å (double nucleus transitionn'Fe (energy ofa particular e)

14.4 keV

255OCiated with

a

famous

high

resolution spectroscopic

method of sodium)

Wavelength is of the

Frequency is of the

order of 102 m,

order of 10-2

radio

wave.

short radio

wave.

i.e., short

Hz, i.e,.

0.29 0 . 0 9 cm=0.0009

i.e., order of 10 wavelength is of the i.e., order of 10m,

ofthe

hc

hc

Energy =or e

Energy Xe

=

W

= 100 x.265 = 26.5

m EXAMPLE 7 . 4 emitted by hydrogen in interstellar The 21 cm radio wave the interaction called the hypertine interaction space is due to of the emitted wave is nearly is atomic hydrogen. the energy

x3x10*

14.4x10 x1.6x10-19

1.e., A= 0.86 x 10-0 8.6 x 10-

m

(2) 1 joule

(1) 10-7joule

4) 10 joule

(3) 7x 10 joule

="=O.6 X10*x

3x10S

=

0.94 x 102= 10-24 J

21x10

EXAMPLE 7 . 5 microwave.

visible

radiations.

The oscillating electric and magnetic

vectors

of an

electromagnetic wave are oriented along

(1) The same direction but differ in phase by 9o° (2) The same direction and are in phase (3)

a= 6.63x10-

A/m.

E, 100 V/m, B,=0.265 Sol (1) Here Maximum rate of energy flow S =E, x B,

m

m,

avelengths are

(2) 36.5 W/m (4) 765 W/m

(1) 26.5 W/m2 (3) 46.7 W/m

Sol.(4)E

(c) T=0.29 or

ie., X-rays.

(4) pressure radiant

associated with

contexts

interstellar space)

d)

(2) electric current

field give rise to magnetic field

(wavelength

0.29

electric field

propagation contains of electric direction. Thus the changing perpendicular in mutually

radiation in different

State the part of the

changing

a

waves

LLUSTRATION 7 . 7

Given below

to Maxwell's hypothesis,

(1) an e.m.f. (3) magnetic field

at 10 m

4xTx10

4Tr

3x10

gives riseto

radiation Average intensity of Power

C

m

4xTx1

4Tr

=6x10*T

B==

Sol (2) c=

5 W

a)Visible

4

(4) 11 1 0 - T

(3) 9x 10 T

ellechon.

(a) 21

(2) 6x 10-*T

(1) 4x 10-T

Assumet h a t

b)

with to oscillate oscil|lating

the electric field was found of the an amplitude of 18 V/m. The magnitude magnetic field will be In an apparatus,

the bulb?

the radiation is emitted isotropicailly and neglect

At a

Solved Examples

of a 100 W ligh bulb is converted

About

7.5

Mutually perpendicular directions and are

in

phase

(4) Mutually perpendicular directions and differ in phase by 90°

w

(3) Ë and B are mutually phase i.e. they become zero and are place and at the same time.

perpendicular to and

each other

minimum at the same

7.6 Magnetism

and

Electromagnetic Induction The

EXAMPLE 7.6 In which

one of the following regions of the electromagnetic to spectrum will the vibrational motion of molecules give rise

absorption

EXAMPLE

(2) microwaves

by

(4) radio waves

region of EM-spectrum. Due

Kirchhoff's

to

-

wave

law

(3) E,B,

Sol Bo

EXAMPLE 7 . 7 or

electromagnetic wave travels along z-axis. Which would the following pairs of space and time varying fields An

generate such a wave

wave travelling8 Sol. (1) E, and B, would generate a plane EM in z-direction. E, B and k form a right handed system k is along

z-axis. As ixj=k Ck i.e. E is

along x-axis and B is along y-axis.

signal

by point

from a certain point in the form of surface of the

an antenna

emitted

received at another

(4) None of these

by

receiving

the

antenna

EXAMPLE 7 . 9 The electromagnetic waves do not transport

(2) charge

EM

SolL (2)

=-

and =27tv

7.13

HV

(1)

2x5x10-16

E

at a distance place.

(1) enerEy

217t

also k

8.85

= 0.61x10 Im

(4) both (1) and (2)

antenna and received

transmitting

Whichdescriofbedthe

can be

both are amplitude Sol (4) Ground wave and sky wave modulated signal is transmitted modulated wave and the amplitude a

).

-

antenna that is 2 m long is oriented at A radio receiver wave and receives a siona the direction of the electromagnetic The maximum ínstantane W/m. x 1010 of intensity 5 ends of the antenma is two the across potential difference V 1.23 (4) 12.3 mv 1.23 (2) 1.23 mV (3)

(2) ground wave

(1) sky wave (3) sea wave

by

vaculum

Sol. (1)I=;%CE%

EXAMPLE 7.8 A

sin(kx

These relation gives E R = B,a0

EXAMPLE

(1) E, B, (2) E, B, (3) E, B, 4) E, B

B,

(2) E,= B,k

ak

Eo=C.

=

=

(1) Ek=B,o

in

spectroscopy the same will be absorbed.

E i xB,j

gOing through

); B

is true following equation

(2) Molecular spectra due to vibrational motionlie in the

microwave

C

7. 1 2

sin(kx

E E

= constant

VIT

An electromagnetic

(1) ultraviolet (3) infrared Sol.

-

ratio&= 27 27v

(3)

transport

waves

(4) information

momentum

momentum

energy,

and

information but not charge. EM waves are uncharged

Also

Eo

o

=

E,d = 0.61 x 10 x 2=123 pV

EXAMPLE 7 . 1 4 which has relave Electromagnetic waves travel in a medium 2.14. Then thesped permeability 1.3 and relative permittivity will be medium the in wave of the electromagnetic x m/s 10 (1) 13.6x 10 m/s (2) 1.8 x (3) 3.6x 10 m/s (4) 1.8 10 m/s

Sol.4) v= uE

3x10

V1.3x2.14

= 1.8 x 10 m/s

EXAMPLE 7 . 1 0 A

plane electromagnetic wave

If the

wave

p 0 , E= 0

Sol.

(2)

pressure

on

a

delivers momentum p and energy

(1) p=0, E =0 (3)

is incident on

EM

E, then

EXAMPLE 7 5 speed of electromagnetic waves in

(2) p 0 , E 0

Ifc is the

(4) p=0, E+0

in a medium

of dielectric

constant

carry

They

momentum and hence can exert

also transfer energy to the surface so

(2) v=cyu,K

(1) v=

K

(3) v=-

EXAMPLE 7.11

An electromagnetic wave, going through sin(lr or). Which of the following is

vacuum

by E E

independent

wave

The angular

length.

(4) kw

(3) k/o

(2)

C

K

is described

of wavelength

Sol. (3)

zabihiy

K and relative pernca

P:0 and E +0.

1)k

speed

vacuum, 1s

, is

waves

surfaces.

material surface.

4)

C and

Sol, (3) Speed of light of vacuum

c=

medium V=-

VHE wave

number k

is The angular frequency

=

a=

27v.

where A is the

C

VHofo

in another

CXercISes

n g l eC o r r e c t

13. A plane electromagnetic wave

Answer Type

E= 100 cos(6 x 10*1 + 4x) V/m

v of sunlight (in W/m) at the solar surface will be I. The

S.6 x

()

4.2 x

() .

10 10

of the

(2) 5.6 x 10 (4) 4.2x 107

(3) 2.4

following has zero average value in a plane

Which electromagnetic wave?

(2) Magnetic potential (4) Magnetic energy (3) Electric energy impedance of free space is The wave (1) Electric field

The frequency

105/ MHz of radiation

levels in close energy

( ) radio waves

hydrogen belongs (2) infrared waves

associated with , The wave

6.

from two

to

(3) micro waves

(2) micro waves

(3) ultraviolet ways

(4) infrared waves

its

(4) wavelength

7. The shortest wavelength of X-rays remitted from an X-ray

e,

8. A-rays are not used for radar purposes, because they are not

(1) reflected by target 2) partly absorbed by target

and p, represent the permittivity and

permeability

medium, the refractive index of the medium

of

is

(2) (4)Eo

Ve field oscillates

plane electromagnetic wave, the electric and amplitude sinusoidally at a frequency of 2.5 x 100 Hz field 480 V/m. The amplitude of the oscillating magnetic a

1.52

x

10* Wb/m?

capacitance

(1)2x 109 Hz

10-l6 J. Its (2) 5 x 10* Hz

(3) 5x 107 Hz

(4) 5x 10i6 Hz

frequency

is

(4) hcleV

10-7 Wb/m

pf

(2) 1.5 T (4) 0.15 T

sinusoidal plane wave

E 36 sin (1.20 x 10':- 3.6 x 10") V/m The average intensity of beam in W/m* will be (2) 3.44 (1) 6.88 (3) 1.72

will be

(3) eVlch

10-7 Wb/m

x

x

=

l0. In X-ray tube, the accelerating potential applied at the anode Is V volt. The minimum wavelength of the emitted X-ray (2) hleV

1.6

18. A flood light is covered with a fitter that transmits red light. The electric field of the emerging beam is represented by a

(4) completely absorbed by target

1)eVih

1.52

tion current of 0.15 A is (3) 15T

.Theenergy of X-rays photon is 3.3x

(2) (4)

17. The magnetic field between the plates of radius 12 cm separated by a distance of 4 mm of a parallel plate capacitor of 100 along the axis of plates having conduc(1) zero

(3) electromagnetic waves

(4) 0.86

19. The average energy-density of electromagnetic wave given by E= (50 N/C) sin(( - kr) will be nearly

I h e area of television telecast is made twice, the height of antenna will be changed as

gnetic (1) 36.6 m (3) 42.3 m

of a

(4) Ko

(3) 1.6 x 10-6 Wb/m

the tube

(3) current in the tube (4) nature of target of the tube

x

the dielectric constant

(2)

(3)

(1)

(1) nature of the gas in the tube

quency 8.2

K,

will be

tube depends upon

(1) halved 3) quardupled 12. If aa Source is source

and

vacuum and e and u represent the permittivity and perme

16. In

(2) intensity

2) voltage applied to

1

(1) Foo E

The percentage power of X-ray increases with the increases

(1) velocity 3) frequency

permeability

medium, its refractive index is given by

ability of given by

(4) rays 2.7 K belongs to

(1) radio waves

be the

4,

15. If

arising

(2) 2.0 (4) 4.0

(3) HKo

(4) 3776 2

B) 1883 2

14. If

(1)

(2) 376.6 Q

(1) 0 2

propagates in a medium of dielectric constant () 1.5

(2) doubled

(1) 10* J/m'

(2) 10 J/m

(3) 10 J/m

(4) 10 J/m

20. A larger parallel plate capacitor, whose plates have an area

(4) kept unchanged

of I m are separated from each other by I mm. If the plates

transmitting electromagnetic wave of lre-

has dielectric constant 10, then the displacement current at this instant is

of the clectro-

106 Hz, then the wavelength transmitted from the source will be

waves

(2) 40.5 m (4) 50.9 m

(1) 25 uA

(2) 11 uA

(3) 2.2 uA

(4) 1.1 MAA

7.8

Magnetism

21. A

and

Electromagnetic Induction

parallel plate capacitor with plate area A and

between the plates d, is charged by a constant separationi. current Consider a plane surface of area A/2 to the plates parallel and drawm simultaneously between the The (1) i

displace

plates.

ment current through this area is

(2) i/2 (4) i/8

(3) i/4

23. The average value of electric energy

density

in

magnetic wave is (E, is peak value)

an

electro

roof willbe

25. In Q. 24, the radiation foree on the (1) 8.53 x 105 N (2) 2.3x 10-3 N (3) 1.33 x 10*N 4) 5.33 x 10 N

of

wavelength 5900 A emitted by any atom or molecule must have some finite total length which is known as coherence length. For sodium light, this length is 2.4 cm. The number of oscillations in this length will be

(2) 4.068 x 10

point

2)r 3

4

(3)

2r kes a

(2) 1.33 x 10-1' N (4) 6.6 x 10-10 N

time is E = (80i +32j-64k) V/m and the magnetic field is

B (0.2i +0.08j-0.29k)uT. The pointing vector for these fields is

(1) -11.52i +28.8j (3) 28.8i-11.52j

(2) -28.8i+11.52i

4) 11.52i-28.8

tion has wavelength of 60 mm. The electric field is in the y-direction and its maximum magnitude is 33 V/m. The equation for the electric field as function ofx and t is (1) 11 sin {t- xlc) (2) 33 sin Tx 10"(t-xlc) (3) 33 sin r(t- xlc) (4) 11 sin Tx 10"(t-xc) 34. In an electromagnetic wave, the electric field oscillated

sinusoidally with amplitude 45 Vm', the rms value of oscil-

lating magnetic field will be (1) 1.6 x 10- T

(2) 16 x 10° T

(3) 144x 10-T

4) 11.3x 10-T

35. The magnetic field in the plane electromagnetic wave s

B=2x 107 sin(0.5 x 10x + 1.5x 10 1)tesla.

a

The

expression for electric field

will be (1) E = 30V2 sin(0.5 x 10 x+1.5x10") V/m

(2) E

.

60 sin(0.5 x 10x + 1.5 x 10"1) V/m

(4) 3.3 x 10-13 T

transmitting antenna of a radio-station is mounted verAt a

tically.

(1)

given by

(4) 4.068 x 10

maximum electric field intensity of 104 Vm' on arrival at a receiving antenna. The maximum magnetic fux density of such a wave is (1) zero (2) 3 x 10* T

29. The

B

field in the ring is

33. A plane electromagnetic wave propagating in the zdirec-

26. A plane electromagnetic wave of wave intensity 6 W/m2 strikes a small mirror of area 39 cm?, held perpendicular to the approaching wave. The momentum transferred in kg ms by the wave to the mirror each second will be (1) 1.2x 10-10 (2) 2.4x 10 (3) 3.6 x 10-* (4) 4.8 x 10-7

(3) 5.8x 10 T

ri

32. In a region of free space the electric field at some instant of

earth's surface. The total power that is incident on a roof of dimensions 8 mx 20 m will be (2) 6.4 x 105 W (1) 2.56 x 10 W 3) 4.0 x 10' W (4) 1.6x 10 W

radiowave has

with time

according to the equation a constant andi is the time. is K where Ki, The ectric changes

(1) 6.6 x 10- N (3) 1.33x 10-10 N

24. The sun delivers 103 W/m2 of electromagnetic fiux to the

28. A

homogeneous the

approaching wave. The radiation force on the mirror will he

4)E

(1) 4.068 x 10 (3) 4.068 x 10

radius r 1s placed in a 30. A circular ring of magnetic field perpendicular to the plane of

small mirror of area 20 cm', held perpendicular to the

2E

wave

(4) 3x 10T

(3) 10 T

31. A plane em wave of wave intensity of 10 W/m?

(2)

27. The

(1)

The field B

22. The sum delivers 10* W/m2 of electromagnetic flux to the earth's surface. The total power that is incident on a roof of dimensions (10x 10)) m will be (1) 10* W (2) 10' W (3) 10 W (4) 10' W

3) EE

peak electric field is 10 V/m. The amplitude ofthe r e radiated magnetic field is (2) 3.33x 10-12 T 3.33 x 10-10 T

10 km due north of the

transmitter the

(3) E, =30/2 sin(0.5 x 10 x+0.5x 10*1) V/m (4) E,

60 sin(0.5 x 10x + 1.5 x 10"/) V/m

Electromagnetic Waves

7.9

Archives 4.

Correct Answer Type

(1)

has the electric and are which always perpendicular to feld E and B, of polarization is given by X and other The lirection romagnetic

in

wave

at

of wave

propagation

by k.

(AIEEE 2012)

peak

travelling electromagnetic wave The peak value of electric field nl. 20 of value neld in a

(2) 9 V/mn (4) 3 V/m

(3) 12 V/m

List-l (Electromagnetic 3 Match

wave

(JEE Main 2013)

type)

and select the correct

association/application) the the choices given below

(its

option from

E

wave

(JEE Main 2015) The electric fields from air enters a medium.

Eo1*cos

=

E

(i) To treat muscular strain

(B) Radiowaves

ii) For broadcasting

(C) X-rays

(i11) To detect fracture

of

2E-i air

=

Eop cos k(2-cr)

of the following options is

(iv) Absorbed by the ozone layer of the atmosphere

(C) 1) (ii) (ii) (iv)

(B) (i) i) (ii) (i)

(D) (iv) (iv) (i)

in medium

their and frequency v refer to where the wave number k and if E,refer E, values in air. The medium is non-magnetic, and medium respectively. air of to relative permittivities which

bones

(A) (1) (ii) (2) ) (3) iv) 4) i)

(4) 7.75 V/m

lists:

(A) Infrared waves

D) Ultraviolet rays

energy

(JEE Main 2014)

are

List II

List I

magnetic

is half of the

energy

(2) 2.45 V/m

(3) 5.48 V/m

6. An EM

with List-II

zero.

m from the diode is (1) 1.73 V/m

strength is

(1)6V/m

density

a

to the magnetic energy are

Electric energy

in

density. around it. The at 0.1 watt uniformly 5. A red LED emits light distance of l field of the light at a amplitude of the electric

x

,Themagnetic

density is equal

density. (4)

andand k| BxE (2) X'| Ë and || Ë B Ë K B and k||ExB (4) X || and |BxE

Electric energy

waves

densities (2) Both electric and magnetic energy the magnetic of double is (3) Electric energy density

Then

that e

has a

propagation of electromagnetic

density.

vacuum

Ai each

the

medium:

f E MAIN

single

During

E2

correct

(2)=4

2

3) S=2

(4) (JEE Main 2018)

(iii) (JEE Main 2014)

Answers Key EXERCISES ingle Correct Answer Type

1.2) 6.(3)

2.(1) 7.(2)

11.(2) 16.(3) 21.(2)

12. (1) 17. (1) 22. (3)

26.(1)

27.(2)

28. (4)

29. (2)

30. 3)

31.(3)

32.(4)

33. (2)

34.(4)

35.(4)

5.(2) 10.(4)

ARCHIVES

14. (3)

15.(2)

19. (1)

20. (3)

Single Correct Answer Type

3. (3)

4. (1)

8. (1) 13. (2) 18. (3) 23. (4)

9. (3)

24. (4)

25.(4)

JEE Main

.(2) 6.(4)

2.(1)

3. (2)

4. (1)

5.(2)