Suppose that the electric field part of an electromagnetic wave in vacuum is `E={(3.1 N//C) cos [(1.8 rad//m)y+(5.4xx10^(6)rad//s)t]}hat(i)`.
a. What is the direction of propagation ?
b. What is the wavelength `lambda` ?
c. What is the frequency `upsilon` ?
d. What is the amplitude of the magnetic field part of the wave ?
e. Write an expression for the magnetic field part of the wave.

Explanation

a. `-j`
b. We have `E={3.14 N//C cos (1.8 rad//m)y+5.4xx10^(6)rad//s t}t`
The standard equation is `x=A sin [(2pi)/(T)t+(2pi)/(lambda)y]`
Comparing the above equation, `(2pi)/(lambda)y=1.8y`
`lambda = (2xx3.14)/(1.8)=3.5 m`
c. We have `(2pi)/(T)t=5.4xx10^(6)t`
`(1)/(T)=(5.4xx10^(6))/(2xx3.14)`
`upsilon = 0.859xx10^(6)Hz`
d. `c=(E_(0))/(B_(0))`
`B_(0)=(E_(0))/(c )=(3.1)/(3xx10^(8))=(3.1xx10^(-8))/(3)=1.03xx10^(-8)T`
e. `B={(1.03xx10^(-8)T)cos (1.8 rad//m)y+(5.4xx10^(6)rad//s)t}hat(k)`