The electric field associated with an e.m. wave in vacuum is given by
Ē = 40 cos (kz - 9 x 108t) î,
where E, z and t are in volt/m, meter and seconds
respectively. The value of wave constant k is :
(1) 6m-1
(2) 3m-1
(3) 2m-1
(4) 0.5m-1
Answers
Answer:
The electric field associated with an electromagnetic wave in vacuum is given by ∣
E
∣=40 cos(kz−6×10
8
t), where E, z and t are in volt per meter, meter and second respectively. The value of wave vector k is:
MEDIUM
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ANSWER
Given: The electric field associated with an electromagnetic wave in vacuum is given by ∣
E
∣=40cos(kz−6×10
8
t)
To find: Value of wave vector k
Solution:
We know electromagnetic wave eqution is
∣
E
∣=E
0
cos(kz−ωt)
And given equation is
∣
E
∣=40cos(kz−6×10
8
t)
By comparing these two, we get
ω=6×10
8
and
E
0
=40
We also know,
Speed of electromagnetic wave is given by:
v=
k
ω
where v is the speed of the light.
Hence,
k=
v
ω
⟹k=
3×10
8
6×10
8
⟹k=2m
−1
Option (A) is correct.
Explanation: