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A plane electromagnetic wave travelling ...

A plane electromagnetic wave travelling along X - direction has electric field of amplitude `300 Vm^(-1)`, directed along the Y - axis (a) What is the intensity of the wave ? (b) If the wave falls on a perfectly absorbing sheet of area `3.0 m^(2)`, at what rate is the momentum delivered to the sheet and what is the radiation pressure exerted on the sheet ? `[epsilon_(0)=8.854xx10^(-12)C^(2)N^(-1)m^(-2), c=3xx10^(8)ms^(-1)]`

Text Solution

Verified by Experts

For electromagnetic wave propagation in X - direction,
`vec(E )_(0)=300 hat(j)V//m`
`epsilon_(0)=8.85xx10^(-12)C^(2)//Nm^(2)`
`c=3xx10^(8)m//s`
(a) Intensity of wave
`I=epsilon_(0)c E_(rms)^(2)`
`=(epsilon_(0)c E_(0)^(2))/(2)`
`=(8.854xx3xx300xx300xx10^(-12)xx10^(8))/(2)`
`=119.529 W//m^(2)`
(b) Radiation pressure exerted on the sheet
`P=("energy (U)")/(c )=(IA)/(c )=(IA)/(c ) " "` (Area `A=3m^(2)`)
`=(119.529xx3)/(3xx10^(8))=1.195xx10^(-6)N`
Radiation pressure `=("force")/("area")=("momentum"xx"time")/("area")`
`therefore` Pressure `P=(1.19xx10^(-6))/(3)=3.98xx10^(-7)Pa`
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