Question

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​

Answer 1

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: