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In a plane electromagnetic wave, the ele...

In a plane electromagnetic wave, the electric field oscillates sin usoidally at a frequency of `2.0xx10^(10)` Hz and amplitude 48 V `m^(-1)`.
a. What is the wavelength of the wave ?
b. What is the amplitude of the oscillating magnetic field ?
c. Show that the average energy density of the E field equals the average energy density of the B field. `[c=3xx10^(8)ms^(-1)]`.

Text Solution

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a. `lambda = (c )/(upsilon)=(3xx10^(8))/(2xx10^(10))=1.5xx10^(-2)m`
b. `c=(E_(0))/(B_(0)), B_(0)=(E_(0))/(c )=(48)/(3xx10^(8))=16xx10^(-8)T`
c. `U_(E )=(1)/(2)epsilon_(0)E^(2), U_(B)=(1)/(2mu_(0))B^(2)`
But `E=cB, c=(1)/(sqrt(mu_(0)epsilon_(0))) therefore U_(E )=U_(B)`
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