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Suppose that the electric field amplitud...

Suppose that the electric field amplitude of an electromagnetic wave is `E_(0)=120` N/C and that its frequency is `upsilon = 50.0` MHz.
a. Determine, `B_(0), omega, k`, and `lambda`.
b. Find the expressions for E and B.

Text Solution

Verified by Experts

`E=120 NC^(-1), upsilon =50 MHz = 50xx10^(6)Hz`
a. `B_(0)=(E_(0))/(c )=(120)/(3xx10^(8))=4xx10^(-7)T`
`omega = 2pi upsilon = 2xx3.14xx50xx10^(6)=3.14xx10^(8)rad s^(-1)`
`c=(omega)/(k)therefore k=(omega)/(c )=(3.14xx10^(8))/(3xx10^(8))=1.05 rad m^(-1)`
`lambda = (2pi)/(k)=(2xx3.14)/(1.05)=5.98 m`
b. `E=E_(0)sin (k x - omega t)=120 sin (1.05 x-3.14xx10^(8)t)Vm^(-1)`
`B=B_(0)sin (k x-omega t)=4xx10^(-7)sin(1.05x -3.14xx10^(8)t)T`.
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