Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

The magnetic field of an electromagnetic wave is given by B=1.6×106cos(2×107z+6×1015t)(2i+j)Wbm2
​The associated electric field will be:-
A. E=4.8×102cos(2×107z+6×1015t)(i2j)Vm
B. E=4.8×102cos(2×107z6×1015t)(2i+j)Vm
C. E=4.8×102cos(2×107z6×1015t)(2j+i)Vm
D. E=4.8×102cos(2×107z+6×1015t)(i+2j)Vm

Answer
VerifiedVerified
489k+ views
2 likes
like imagedislike image
Hint: An electromagnetic wave is generated from a charged particle that produces an electric field. When it accelerates, it generates ripples and a magnetic field is also formed. This leads to the development of an electromagnetic wave.

Formula used: c=EB, where c is the velocity of light, E is the electric field and Bis the magnetic field.

Complete answer:
The standard form for magnetic field of an electromagnetic wave is given by
B(x,t) = Bmaxcos(kx  ωt + φ).
We are given the vector form of B that is
B=1.6×106cos(2×107z+6×1015t)(2i+j)Wbm2
We know that c=EB
Hence, magnitude of E is given by E=cB=3×108×1.6×106
=4.8×102
We know that the electromagnetic waves is transverse wave means amplitude of waves is perpendicular to the direction of propagation and both these vectors are perpendicular to the propagation vector.
E.B=0
⇒ either direction of E is i2j or i+2j
from given option
Also wave propagation direction is parallel to E×B which is (k)
Hence we can say that the electric field is along i2j.

Combining the results that we obtained from the magnitude calculation and the direction analysis,
The value of E=4.8×102cos(2×107z+6×1015t)(i2j)Vm

So, the correct answer is Option A .

Note:
Both magnetic and electric fields in an electromagnetic wave will vary with time, one leading the other to change.
Electromagnetic waves are considered to be ubiquitous like light and widely utilized in modern technology that includes AM and FM radio, phones including cordless and cellular, door openers for garages , wireless networks, microwave ovens, RADAR etc.

Latest Vedantu courses for you
Grade 10 | CBSE | SCHOOL | English
Vedantu 10 CBSE Pro Course - (2025-26)
calendar iconAcademic year 2025-26
language iconENGLISH
book iconUnlimited access till final school exam
tick
School Full course for CBSE students
PhysicsPhysics
Social scienceSocial science
ChemistryChemistry
MathsMaths
BiologyBiology
EnglishEnglish
₹38,500 (9% Off)
₹35,000 per year
Select and buy